Question

question
solve for x. round to the nearest tenth, if necessary.
triangle image with right angle at u, angle at t is 70°, side ut is 64, side vu is x

Explanation:

Step1: Identify trigonometric ratio

In right triangle TUV, side TU=64 is adjacent to 70°, x=TV is hypotenuse. Use cosine: $\cos(70^\circ)=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{64}{x}$

Step2: Solve for x

Rearrange: $x=\frac{64}{\cos(70^\circ)}$

Step3: Calculate value

$\cos(70^\circ)\approx0.3420$, so $x\approx\frac{64}{0.3420}\approx187.1$

Answer:

187.1