s∈θ = opposite side/hypotenuse
cosθ = adjacent side/hypotenuse
tanθ = opposite side/adjacent side
s∈²θ + cos²θ = 1
Area of triangle = (1/2) × base × height
Perimeter of triangle = sum of all sides
(a/b) = (sinA/sinB) = (s∈α/s∈β) ∈ a triangle with sides a, b and angles A, B
tan(A + B) = (tanA + tanB)/(1 - tanA × tanB)
s∈(A + B) = sinA × cosB + cosA × sinB
cos(A + B) = cosA × cosB - sinA × sinB
s∈(2θ) = 2 × s∈θ × cosθ
cos(2θ) = cos²θ - s∈²θ
tan(2θ) = 2 × tanθ/(1 - tan²θ)

🪤 The 5 Mistakes That Cost Marks

Not checking if the given triangle is right-angled or not
Forgetting to apply the formula (a/b) = (sinA/sinB) = (s∈α/s∈β) ∈ a triangle
Not using trigonometric identities like s∈²θ + cos²θ = 1
Incorrectly applying the formula for area and perimeter of a triangle
Not using the correct trigonometric ratio for a given angle

✏️ 3 Solved PYQs

In a triangle ABC, ∠B = 90°, AB = 8cm and BC = 6cm. Find the length of AC. Step 1: Apply Pythagoras theorem, AC² = AB² + BC² Step 2: Put the values, AC² = 8² + 6² Step 3: Calculate AC², AC² = 64 + 36 = 100 Step 4: Find AC, AC = √100 = 10cm
In a triangle PQR, ∠Q = 90°, PQ = 3cm and QR = 4cm. Find the length of PR. Step 1: Apply Pythagoras theorem, PR² = PQ² + QR² Step 2: Put the values, PR² = 3² + 4² Step 3: Calculate PR², PR² = 9 + 16 = 25 Step 4: Find PR, PR = √25 = 5cm
In a triangle XYZ, ∠Y = 90°, XY = 5cm and XZ = 13cm. Find the length of YZ. Step 1: Apply Pythagoras theorem, XZ² = XY² + YZ² Step 2: Put the values, 13² = 5² + YZ² Step 3: Calculate YZ², 169 = 25 + YZ² Step 4: Find YZ², YZ² = 169 - 25 = 144 Step 5: Find YZ, YZ = √144 = 12cm

🧠 The One Thing Most Students Get Wrong

Most students get wrong the application of trigonometric ratios ∈ a right-angled triangle.
They often confuse the ratios and apply the wrong one, leading to incorrect results.
It is essential to understand and remember the trigonometric ratios and their application ∈ a right-angled triangle.
Students should practice solving problems to become proficient ∈ applying these ratios.

👁️ Ayush's Note

To excel ∈ triangles, focus on understanding and applying trigonometric ratios and identities.
Practice solving problems regularly to become proficient ∈ applying these concepts.
Make sure to check the type of triangle (right-angled, isosceles, equilateral) before applying any formula.
Use the formula (a/b) = (sinA/sinB) = (s∈α/s∈β) to find the length of sides ∈ a triangle.
Remember the Pythagoras theorem and apply it to find the length of the hypotenuse ∈ a right-angled triangle.

🔁 Last 5 Minutes Box

Check all formulas and theorems related to triangles.
Go through the solved examples and practice problems.
Make sure to understand and apply the trigonometric ratios and identities.
Check the type of triangle and apply the relevant formulas.
Practice, practice, practice to become proficient ∈ solving triangle problems.

📝 Practice MCQs

1. In a triangle ABC, ∠B = 90°, AB = 8cm and BC = 6cm. Find the length of A C.

A) 6cm

B) 8cm

C) 10cm

D) 12cm

Answer: C) 10cm. Using Pythagoras theorem, AC² = AB² + BC² = 8² + 6² = 100, so AC = √100 = 10cm.

2. In a triangle PQR, ∠Q = 90°, PQ = 3cm and QR = 4cm. Find the length of PR.

A) 3cm

B) 4cm

C) 5cm

D) 6cm

Answer: C) 5cm. Using Pythagoras theorem, PR² = PQ² + QR² = 3² + 4² = 25, so PR = √25 = 5cm.

3. In a triangle XYZ, ∠Y = 90°, XY = 5cm and XZ = 13cm. Find the length of YZ.

A) 10cm

B) 12cm

C) 13cm

D) 14cm

Answer: B) 12cm. Using Pythagoras theorem, XZ² = XY² + YZ² = 13² = 5² + YZ², so YZ² = 169 - 25 = 144, YZ = √144 = 12cm.

4. If s∈θ = 3/5, find the value of cosθ.

A) 3/5

B) 4/5

C) 3/4

D) 2/3

Answer: B) 4/5. Using the identity s∈²θ + cos²θ = 1, we get (3/5)² + cos²θ = 1, so cos²θ = 1 - (9/25) = 16/25, cosθ = √(16/25) = 4/5.

5. In a triangle ABC, ∠B = 90°, AB = 8cm and BC = 6cm. Find the value of sin A.

A) 3/5

B) 4/5

C) 6/10

D) 8/10

Answer: C) 6/10 or 3/5. sinA = opposite side/hypotenuse = BC/AC = 6/10 = 3/5.

🚀 Ready to Ace Your Exam?

Put your knowledge to the test! Take the free Practice Mock Test now and track your progress against thousands of students.

🎬 Watch video explanations on YouTube →

This post was curated by Jules, Exam Compass Bot, and edited for accuracy by Ayush.

📚 Related Topics

Continue your revision with these related guides:

s∈θ = opposite side/hypotenuse
cosθ = adjacent side/hypotenuse
tanθ = opposite side/adjacent side
s∈²θ + cos²θ = 1
Area of triangle = (1/2) × base × height
Perimeter of triangle = sum of all sides
(a/b) = (sinA/sinB) = (s∈α/s∈β) ∈ a triangle with sides a, b and angles A, B
tan(A + B) = (tanA + tanB)/(1 - tanA × tanB)
s∈(A + B) = sinA × cosB + cosA × sinB
cos(A + B) = cosA × cosB - sinA × sinB
s∈(2θ) = 2 × s∈θ × cosθ
cos(2θ) = cos²θ - s∈²θ
tan(2θ) = 2 × tanθ/(1 - tan²θ)

🪤 The 5 Mistakes That Cost Marks

Not checking if the given triangle is right-angled or not
Forgetting to apply the formula (a/b) = (sinA/sinB) = (s∈α/s∈β) ∈ a triangle
Not using trigonometric identities like s∈²θ + cos²θ = 1
Incorrectly applying the formula for area and perimeter of a triangle
Not using the correct trigonometric ratio for a given angle

✏️ 3 Solved PYQs

In a triangle ABC, ∠B = 90°, AB = 8cm and BC = 6cm. Find the length of AC. Step 1: Apply Pythagoras theorem, AC² = AB² + BC² Step 2: Put the values, AC² = 8² + 6² Step 3: Calculate AC², AC² = 64 + 36 = 100 Step 4: Find AC, AC = √100 = 10cm
In a triangle PQR, ∠Q = 90°, PQ = 3cm and QR = 4cm. Find the length of PR. Step 1: Apply Pythagoras theorem, PR² = PQ² + QR² Step 2: Put the values, PR² = 3² + 4² Step 3: Calculate PR², PR² = 9 + 16 = 25 Step 4: Find PR, PR = √25 = 5cm
In a triangle XYZ, ∠Y = 90°, XY = 5cm and XZ = 13cm. Find the length of YZ. Step 1: Apply Pythagoras theorem, XZ² = XY² + YZ² Step 2: Put the values, 13² = 5² + YZ² Step 3: Calculate YZ², 169 = 25 + YZ² Step 4: Find YZ², YZ² = 169 - 25 = 144 Step 5: Find YZ, YZ = √144 = 12cm

🧠 The One Thing Most Students Get Wrong

Most students get wrong the application of trigonometric ratios ∈ a right-angled triangle.
They often confuse the ratios and apply the wrong one, leading to incorrect results.
It is essential to understand and remember the trigonometric ratios and their application ∈ a right-angled triangle.
Students should practice solving problems to become proficient ∈ applying these ratios.

👁️ Ayush's Note

To excel ∈ triangles, focus on understanding and applying trigonometric ratios and identities.
Practice solving problems regularly to become proficient ∈ applying these concepts.
Make sure to check the type of triangle (right-angled, isosceles, equilateral) before applying any formula.
Use the formula (a/b) = (sinA/sinB) = (s∈α/s∈β) to find the length of sides ∈ a triangle.
Remember the Pythagoras theorem and apply it to find the length of the hypotenuse ∈ a right-angled triangle.

🔁 Last 5 Minutes Box

Check all formulas and theorems related to triangles.
Go through the solved examples and practice problems.
Make sure to understand and apply the trigonometric ratios and identities.
Check the type of triangle and apply the relevant formulas.
Practice, practice, practice to become proficient ∈ solving triangle problems.

📝 Practice MCQs

1. In a triangle ABC, ∠B = 90°, AB = 8cm and BC = 6cm. Find the length of A C.

A) 6cm

B) 8cm

C) 10cm

D) 12cm

Answer: C) 10cm. Using Pythagoras theorem, AC² = AB² + BC² = 8² + 6² = 100, so AC = √100 = 10cm.

2. In a triangle PQR, ∠Q = 90°, PQ = 3cm and QR = 4cm. Find the length of PR.

A) 3cm

B) 4cm

C) 5cm

D) 6cm

Answer: C) 5cm. Using Pythagoras theorem, PR² = PQ² + QR² = 3² + 4² = 25, so PR = √25 = 5cm.

3. In a triangle XYZ, ∠Y = 90°, XY = 5cm and XZ = 13cm. Find the length of YZ.

A) 10cm

B) 12cm

C) 13cm

D) 14cm

Answer: B) 12cm. Using Pythagoras theorem, XZ² = XY² + YZ² = 13² = 5² + YZ², so YZ² = 169 - 25 = 144, YZ = √144 = 12cm.

4. If s∈θ = 3/5, find the value of cosθ.

A) 3/5

B) 4/5

C) 3/4

D) 2/3

Answer: B) 4/5. Using the identity s∈²θ + cos²θ = 1, we get (3/5)² + cos²θ = 1, so cos²θ = 1 - (9/25) = 16/25, cosθ = √(16/25) = 4/5.

5. In a triangle ABC, ∠B = 90°, AB = 8cm and BC = 6cm. Find the value of sin A.

A) 3/5

B) 4/5

C) 6/10

D) 8/10

Answer: C) 6/10 or 3/5. sinA = opposite side/hypotenuse = BC/AC = 6/10 = 3/5.

🚀 Ready to Ace Your Exam?

Put your knowledge to the test! Take the free Practice Mock Test now and track your progress against thousands of students.

🎬 Watch video explanations on YouTube →

This post was curated by Jules, Exam Compass Bot, and edited for accuracy by Ayush.

📚 Related Topics

Continue your revision with these related guides: