Question

In ΔQRS, the measure of ∠S=90°, the measure of ∠Q=83°, and RS = 7 feet. Find the length of SQ to the nearest tenth of a foot.

Answer 1

x ~0.9

Explanation:

To solve for (x) in the given right triangle, use the trigonometric ratios, which are the following,

`sin(\theta)=(opposite)/(hypotenuse)\\\\cos(\theta)=(adjacent)/(hypotenuse)\\\\tan(\theta)=(opposite)/(adjacent)`

Each of the sides of a triangle is named with respect to the given angle. In this problem, one is given the side opposite to the given angle, and the side adjacent to it. Use the ratio of tangent (tan) to solve for the unknown side.

`tan(83)=(7)/(x)`

Manipulate the equation so that it is solved for (x),

`x=(7)/(tan(83))`

x ~ 0.859