Question

In right angled ∆ABC, angle A=90° , and the ratio of measure of angle B and angle C is 4:5, find the measure of angle B and angle C?​

Answer 1

Given :

• ABC is a right angled triangle
• angle A = 90°
• angle B : angle C = 4:5

To find:

• angle B
• angle C

Solution:

Let the common ratio be x .

Then ,

• angle B = 4x
• angle C = 5x

Applying angle sum property of a triangle ,

• angle A + angle B + angle C = 180°

90° + 4x + 5x = 180°

90° + 9x = 180°

9x = 180° - 90°

9x = 90°

x = 90° / 9

x = 10

Therefore ,

• angle B = 4 × 10 = 40°
• angle B = 4 × 10 = 40° angle C = 5 × 10 = 50°

____________________________

$\underline{ \underline{ \large{ \mathfrak{ \orange{some }\: \blue{basic }\: \green{concepts : }}}}}$

• A triangle in which one angle measures 90° is called a right angled triangle .
• The side opposite to 90° angle is called hypotenuse . The other two sides are base and perpendicular .
• In right angled triangle , hypotenuse² = Base² + Perpendicular ² (Pythagoras theorem)
• According to angle sum property , sum of all angles in a triangle is 180° .

Answer 2

Answer:

solution : In right angled ∆ ABC,

angle A= 90°

and the ratio of measure of angle B and angle C is 4:5.

Let, angle B=4x & angle C= 5x

According to question , B +C= 90°

then, 4x +5x =90°

9x =90°

x = 10°

so, angle B= 4x= 4×10=40

angle C = 90-40=50