In ΔHIJ, the measure of ∠J=90°, the measure of ∠I=64°, and HI = 5.4 feet. Find the length of JH to the nearest foot.
right triangle, hypotenuse = 5.4
so
sin I = JH/5.4
so
JH = 5.4 sin 64
To find the length of JH, we can use trigonometric ratios in a right triangle. In this case, we have a right triangle ΔHIJ with a right angle at point J.
We are given that the measure of ∠J is 90°, the measure of ∠I is 64°, and HI = 5.4 feet. We need to find the length of JH.
First, let's identify the sides of the triangle. The side opposite to ∠I is JH (which we need to find). The side adjacent to ∠I is HI.
Since we have the lengths of two sides of a right triangle, we can use the trigonometric ratio tangent (tan) to find the length of JH.
The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. In this case, we can use the tangent of ∠I.
The tangent of an angle A is given by the formula: tan(A) = opposite/adjacent.
In our triangle, tan(∠I) = JH / HI.
Plugging in the values we know, tan(64°) = JH / 5.4.
To find JH, we need to isolate it in the equation. Multiply both sides of the equation by 5.4: JH = 5.4 * tan(64°).
Using a calculator, evaluate 5.4 * tan(64°) to get the approximate value for JH.
JH ≈ (5.4) * (1.8017) ≈ 9.72 feet.
Therefore, the length of JH, rounded to the nearest foot, is approximately 10 feet.