Question

The three inside angles (A, B and C) of a right-angled triangle

are in the ratio 7: 18:11
angle B
The smallest angle is 35º.
angle C
Work out angles A, B and C.
Please can someone help me​

Answer 1

The measure of angle A is 35°

The measure of angle B is 90°

The measure of angle C is 55°

Explanation:

Let

x -----> the measure of angle A

y ----> the measure of angle B

z ----> the measure of angle C

we have

`x: y:z=7: 18:11`

Observing the ratio

The smallest angle is x and the greatest angle is y

In a right triangle, the measure of the right angle is the greatest angle and the sum of the other two angles is equal to 90 degrees, because are complementary angles

so

y=90° -----> equation A

x+z=90° -----> equation B (by complementary angles)

x=35° -----> equation C (the smallest angle)

Substitute the value of x in equation B and solve for z

35°+z=90°

z=90°-35°=55°

therefore

The measure of angle A is 35°

The measure of angle B is 90°

The measure of angle C is 55°