Question

find m∠h.
j
7.8
i
3
h
write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠h = °

Explanation:

Step1: Identify triangle type and sides

This is a right - triangle \( \triangle HIJ \) with \( \angle J = 90^{\circ} \), \( HJ = 3 \) (opposite to \( \angle I \)) and \( JI=7.8 \) (opposite to \( \angle H \)). We can use the tangent function to find \( \angle H \). The tangent of an angle in a right - triangle is defined as \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \). For \( \angle H \), the opposite side is \( JI = 7.8 \) and the adjacent side is \( HJ=3 \). So \( \tan(\angle H)=\frac{JI}{HJ}=\frac{7.8}{3} \)

Step2: Calculate the angle

First, calculate \( \frac{7.8}{3}=2.6 \). Then, to find \( \angle H \), we take the arctangent (inverse tangent) of \( 2.6 \), i.e., \( \angle H=\arctan(2.6) \). Using a calculator, \( \arctan(2.6)\approx68.97^{\circ}\approx69.0^{\circ} \) (rounded to the nearest tenth)

Answer:

\( 69.0 \)