Question

Given: ABC is a right triangle with right angle C. AC=15 centimeters and m∠A=40∘.

What is BC ?

Answer 1

To find the length of side BC, we'll use right-triangle trigonometry as follows:

The value of the tangent function for the measure of angle A = (the length of the side opposite angle A)/(the length of the side adjacent to angle A)

tan 40° = BC/AC

tan 40° = BC/15 cm

Now, multiply both sides by 15 cm:

(tan 40°)(15 cm) = (BC/15 cm)(15 cm)

(tan 40°)(15 cm) = (BC)(15 cm/15 cm)

(tan 40°)(15 cm) = (BC)(1)

BC = (tan 40°)(15 cm)

Now, using a table of values for the trigonometric functions for angles from 0° to 90° or using a scientific calculator, we find that tan 40° = .8391 (to 4 decimal places). Now, substituting on the right side we get:

BC = (.8391)(15 cm)

BC = 12.6 cm to the nearest tenth of a centimeter.