Question

Solve for x. Round to the nearest tenth, if necessary.

Answer 1

Answer: $33.2$

Step-by-step explanation:

Given

CE=85

$\angle C=67^{\circ}$

In $\triangle CDE$, using trigonometry

$\Rightarrow \cos 67^{\circ}=\dfrac{CD}{CE}\\\\\Rightarrow CD=CE\cos 67^{\circ}\\\\\Rightarrow CD=85\times \cos 67^{\circ}\\\\\Rightarrow CD=33.2$

Answer 2

Given:

A figure of a right angle triangle.

To find:

The value of x.

Solution:

In a right angle triangle,

$\cos \theta =\dfrac{Base}{Hypotenuse}$

In the given figure,

$\cos C =\dfrac{CD}{CE}$

$\cos 67^\circ =\dfrac{x}{85}$

$0.39073\times 85=x$

$33.21205=x$

Round to the nearest tenth.

$x\approx 33.2$

Therefore, the measure of x is 33.2 units.