find m∠j.\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\nm∠j = □°
find m∠j.\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\nm∠j = □°
Answer
Explanation:
Step1: Recall trigonometric ratio
In right - triangle $\triangle JKI$ with right - angle at $K$, we use the cosine function. $\cos J=\frac{JK}{JI}$. First, find the length of $JI$ using the Pythagorean theorem.
Step2: Apply Pythagorean theorem
In right - triangle $\triangle JKI$, by the Pythagorean theorem $JI=\sqrt{JK^{2}+KI^{2}}$. Given $JK = 2$ and $KI = 5$, then $JI=\sqrt{2^{2}+5^{2}}=\sqrt{4 + 25}=\sqrt{29}$.
Step3: Calculate cosine of angle $J$
$\cos J=\frac{JK}{JI}=\frac{2}{\sqrt{29}}$.
Step4: Find the measure of angle $J$
$J=\cos^{-1}(\frac{2}{\sqrt{29}})$. Using a calculator, $\cos^{-1}(\frac{2}{\sqrt{29}})\approx68.2^{\circ}$.
Answer:
$68.2$