Question

solve for x. round to the nearest tenth, if necessary. triangle image with right angle at h, ih = 4.5, angle at i is 48°, hypotenuse ig is x

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle, with angle $\angle I = 48^\circ$, adjacent side to this angle is $IH = 4.5$, and $x$ is the hypotenuse. Use cosine: $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$

Step2: Substitute known values

$\cos(48^\circ) = \frac{4.5}{x}$

Step3: Rearrange to solve for $x$

$x = \frac{4.5}{\cos(48^\circ)}$

Step4: Calculate the value

First, $\cos(48^\circ) \approx 0.6691$, so $x \approx \frac{4.5}{0.6691} \approx 6.7$

Answer:

$6.7$