Question

Find the value of x. Round to the nearest tenth

Answer 1

`x \approx 7.2`

Explanation:

The given triangle is a right triangle this is indicated by the box around one of its angles, signifying that the angle is a right angle. One of the properties of a right triangle is the right angle trigonometric ratios. these are a series of ratios that relate the sides and angles of a right triangle. Such ratios are as follows:

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

Please note that the sides named (
`opposite`) and (
`adjacent`) Are subjective and change based on the angle by which one refers to. However the side (
`hypotenuse`) indicates the side opposite the right angle, this side does not change its name.

In this case, one is given a (33) degree angle, and the measure of the side adjacent to is, (6). One is asked to find the measure of the hypotenuse (x). It would be most logical to use the ratio of cosine (cos). Substitute the given values in and solve for (x).

`cos(\theta)=(adjacent)/(hypotenuse)`

`cos(33)=(6)/(hypotenuse)`

Inverse operations,

`cos(33)=(6)/(hypotenuse)`

`hypotenuse=(6)/(cos(33))`

`hypotenuse \approx 7.15`

Answer 2

Explanation:

use cos since we're given the adjacent and asked to find the hypothenus.

cos 33° = 6/x

cross multiply

xcos33° = 6

divide both sides by cos 33°

(cos 33 is approximately 0.8387)

then x = 7.15