Question

find hj.
write your answer as an integer or as a decimal rounded to the nearest tenth.
hj =
submit

Explanation:

Step1: Identify the triangle type and trigonometric ratio

We have a right - triangle \( \triangle HIJ \) with \( \angle J = 90^{\circ} \), \( \angle H=26^{\circ} \) and hypotenuse \( HI = 9 \). We want to find the length of \( HJ \), which is the adjacent side to \( \angle H \). The cosine of an angle in a right - triangle is defined as \( \cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}} \). So, \( \cos(26^{\circ})=\frac{HJ}{HI} \)

Step2: Substitute the known values and solve for \( HJ \)

We know that \( HI = 9 \) and \( \theta = 26^{\circ} \). Substituting these values into the cosine formula, we get \( HJ=HI\times\cos(26^{\circ}) \)
We know that \( \cos(26^{\circ})\approx0.8988 \) (using a calculator). Then \( HJ = 9\times0.8988=8.0892\approx8.1 \)

Answer:

\( 8.1 \)