Question

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

A = 33.3◦; b = 3.8m Round side lengths to one decimal place.

A) B = 56.7◦; a = 2.5mc = 4.5m
B) B = 56.7◦; a = 5.0mc = 6.3m
C) B = 56.7◦; a = 1.4mc = 4.0m
D) B = 56.7◦; a = 1.4mc = 5.0m
E) none of the above

*Can you please tell me which one is the right choice, and how did you get that choice?

*Can you explain what is (mc) and how to convert it to (m)?

Answer 1

Option A

`m\angle B=56.7^o`

`a=2.5\ m`

`c=4.5\ m`

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

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

we have

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

substitute

`(3.8)/(sin(56.7^o))=(c)/(sin(90^o))`

`c=(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

`(b)/(sin(B))=(a)/(sin(A))`

we have

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

substitute

`(3.8)/(sin(56.7^o))=(a)/(sin(33.3^o))`

`a=(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