Question

1. solve the triangle:

(image of a right triangle with right angle at c, angle at b is 52.8°, side a = 10.7. below the image: a =, a =; b =, b =; c =, c =)

Explanation:

Step1: Identify known values

Right triangle: $C=90^\circ$, $B=52.8^\circ$, $a=10.7$ (side opposite $A$)

Step2: Calculate angle A

$A=90^\circ - B=90^\circ -52.8^\circ=37.2^\circ$

Step3: Find side b (opposite B)

$\tan B=\frac{b}{a}\Rightarrow b=a\tan B=10.7\times\tan52.8^\circ\approx10.7\times1.327\approx14.2$

Step4: Find side c (hypotenuse)

$\cos B=\frac{a}{c}\Rightarrow c=\frac{a}{\cos B}=\frac{10.7}{\cos52.8^\circ}\approx\frac{10.7}{0.604}\approx17.7$

Answer:

$a=10.7$, $A=37.2^\circ$, $b\approx14.2$, $B=52.8^\circ$, $c\approx17.7$, $C=90^\circ$