Question

Solve the right triangle shown in the figure

Answer 1

Option B

Explanation:

step 1

Find the measure of angle A

Remember that the sum of the interior angles of a triangle must be equal to 180 degrees

∠A+∠B+∠C=180°

substitute the given values

∠A+23.4°+90°=180°

∠A+23.4°+90°=180°-113.4°=66.6°

step 2

Find the length of side BC (a)

Applying the law of sines

c/sin(C)=a/sin(A)

3.3/sin(90)=a/sin(66.6)

a=3.3*sin(66.6)/sin(90)

a=3.0 mm

step 3

Find the length side AC (b)

Applying the law of sines

c/sin(C)=b/sin(B)

3.3/sin(90)=b/sin(23.4)

b=3.3*sin(23.4)/sin(90)

b=1.3 mm