Question

Solve the right triangle. Give angles in degrees and minutes.

Answer 1

Answer:

Option A

$m\angle B=56.7^o$

$a=2.5\ m$

$c=4.5\ m$

Step-by-step explanation:

step 1

Find the measure of angle B

we know that

$m\angle A+m\angle B=90^o$ ----> by complementary angles

we have

$m\angle A=33.3^o$

substitute

$33.3^o+m\angle B=90^o$

$m\angle B=90^o-33.3^o$

$m\angle B=56.7^o$

step 2

Find the measure of side c

Applying the law of sines

$\frac{b}{sin(B)}=\frac{c}{sin(C)}$

we have

$b=3.8\ m\\B=56.7^o\\C=90^o$

substitute

$\frac{3.8}{sin(56.7^o)}=\frac{c}{sin(90^o)}$

$c=\frac{3.8}{sin(56.7^o)}sin(90^o)$

$c=4.5\ m$

step 3

Find the measure of side a

Applying the law of sines

$\frac{b}{sin(B)}=\frac{a}{sin(A)}$

we have

$b=3.8\ m\\B=56.7^o\\A=33.3^o$

substitute

$\frac{3.8}{sin(56.7^o)}=\frac{a}{sin(33.3^o)}$

$a=\frac{3.8}{sin(56.7^o)}sin(33.3^o)$

$a=2.5\ m$

Note: (mc) is not a unit, in the question the options were written without leaving any space

so

B = 56.7◦; a = 2.5mc = 4.5m

instead of

B = 56.7◦; a = 2.5 m; c=4.5 m