Question

find $m\angle b$.

triangle with right angle at c, cd=3.9, cb=7.5

write your answer as an integer or as a decimal rounded to the nearest tenth.
$m\angle b = \square ^\circ$

submit

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( \triangle BCD \) (right-angled at \( C \)), for \( \angle B \), the opposite side to \( \angle B \) is \( DC = 3.9 \) and the adjacent side is \( BC = 7.5 \). So we use the tangent function: \( \tan(\angle B)=\frac{\text{opposite}}{\text{adjacent}}=\frac{DC}{BC} \).

Step2: Calculate \( \tan(\angle B) \)

Substitute \( DC = 3.9 \) and \( BC = 7.5 \) into the formula: \( \tan(\angle B)=\frac{3.9}{7.5}=0.52 \).

Step3: Find \( \angle B \)

Take the arctangent (inverse tangent) of \( 0.52 \): \( \angle B=\arctan(0.52) \). Using a calculator, \( \arctan(0.52)\approx27.5^\circ \) (rounded to the nearest tenth).

Answer:

\( 27.5 \)