Answer:
77.32
Step-by-step explanation:
sin = opposite/hypotenuse
Opposite of A = BC = 80
Hypotenuse = AC = 82
sin A = 80/82
Use a calculator: A = 77.32
Answer: The measure of angle A is 77.32°.
Step-by-step explanation: We are given to find the measure of angle A from the figure provided.
From the figure, we can note that
ΔABC is a right-angled triangle, where
∠B = 90°, AB = 18 units , BC = 80 units and hypotenuse AC = 82 units.
Therefore, from the laws of ratios of trigonometry we have
[tex]\sin m\angle A=\dfrac{perpendicular}{hypotenuse}\\\\\\\Rightarrow \sin m\angle A=\dfrac{80}{82}\\\\\\\Rightarrow \sin m\angle A=0.9756\\\\\Rightarrow m\angle A=\sin^{-1}(0.9756)\\\\\Rightarrow m\angle A=77.3170^\circ\sim 77.32^\circ.[/tex]
Thus, the measure of angle A is 77.32°.
