Question

Please help! Find angle G, angle J, and side GJ. Round your angles to the nearest degree and side GJ as a radical or a decimal number to the nearest tenth.

Answer 1

Answer:

∠G = 50°

GJ = 7.79

Step-by-step explanation:

Trigonometry:

  To find ∠G, we can use Tan ratio.

        $\sf Tan \ G = \dfrac{opposite \ side \ of \ \angle G}{adjacent \ side \ of \ \angle G}\\\\Tan \ G = \dfrac{6}{5}\\\\Tan \ G = 1.2\\\\G = Tan^{-1} \ (1.2)\\\\G = 50.19\\\\ \angle G = 50^\circ$

Now, to find GJ, we can use the trigonometry ratio Sin,

    $\sf Sin \ 50^\circ = \dfrac{opposite \ side }{hypotenuse}\\\\Sin \ 50^\circ =\dfrac{6}{GJ}\\\\0.766 =\dfrac{6}{GJ}\\\\GJ* 0.766 =6\\\\ GJ = \dfrac{6}{0.77}\\\\\\GJ=7.79$