find m∠d. write your answer as an integer or as a decimal rounded to the nearest tenth. m∠d = °
find m∠d. write your answer as an integer or as a decimal rounded to the nearest tenth. m∠d = °
Answer
Explanation:
Step1: Identify trig - ratio
In right - triangle BCD, we know the adjacent side to angle D (CD = 3) and the hypotenuse (BD = 4). We use the cosine function, $\cos(D)=\frac{\text{adjacent}}{\text{hypotenuse}}$. So, $\cos(D)=\frac{3}{4}$.
Step2: Find the angle
To find the measure of angle D, we take the inverse cosine of $\frac{3}{4}$. That is, $D=\cos^{- 1}(\frac{3}{4})$. Using a calculator, $D=\cos^{-1}(0.75)\approx41.4^{\circ}$.
Answer:
$41.4$