Question

In ΔHIJ, the measure of ∠J=90°, HI = 8 feet, and JH = 1.9 feet. Find the measure of ∠H to the nearest tenth of a degree.

Answer 1

Given:

In ΔHIJ,

The measure of ∠J = 90°

HI = 8 feet

JH = 1.9 feet

To find:

The measure of ∠H to the nearest tenth of a degree

Solution:

The following trigonometric function of a triangle will be used to solve the given problem:  

$\boxed{\bold{cos \:\theta = \frac{Adjacent \:side}{Hypotenuse} }}$

Here in Δ HIJ, we have,

θ = ∠H

Adjacent side / Base = JH = 1.9 feet

Hypotenuse = HI = 8 feet

∴   $cos \:\theta = \frac{JH}{HI} }}$

substituting the given values of JH & HI

⇒ $cos \:\theta = \frac{1.9}{8} }}$  

⇒ $cos \:\theta = 0.2375$

⇒  $\theta = cos^-^1 (0.2375)$

⇒ $\theta = 76.260$°

we will round off the value of θ to its nearest tenth of a degree

⇒ $\bold{\theta}$ ≈ $\bold{76.3}$°

Thus, the measure of ∠H to the nearest tenth of a degree is 76.3°.

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