Question

In triangle ABC, A=25, c=55 and AB=60. What are the approximate measures of the remaining side lengths of the triangle?

Answer 1

`a\approx 31`

`b\approx 72`

Explanation:

Please find the attachment.

We have been given that in triangle ABC, A=25, C=55 and AB=60. We are asked to find the approximate measures of the remaining side lengths of the triangle.

We will use Law of Sines to solve for side lengths of given triangle.

`\frac{\text{sin}(A)}{a}=\frac{\text{sin}(B)}{b}=\frac{\text{sin}(C)}{c}`, where a, b and c are opposite sides corresponding to angles A, b and C respectively.

Upon substituting our given values, we will get:

`\frac{\text{sin}(25)}{a}=\frac{\text{sin}(55)}{60}`

`a=\frac{60\text{sin}(25)}{\text{sin}(55)}`

`a=(60*0.422618261741)/(0.819152044289)`

`a=(25.35709570446)/(0.819152044289)`

`a=30.9552980807967304`

`a\approx 31`

Therefore, the measure of side 'a' is approximately 31 units.

We can find measure of angle B using angle sum property as:

`m\angle A+m\angle B+m\angle C=180`

`25+m\angle B+55=180`

`m\angle B+80=180`

`m\angle B=100`

`\frac{\text{sin}(100)}{b}=\frac{\text{sin}(55)}{60}`

`b=\frac{60\text{sin}(100)}{\text{sin}(55)}`

`b=(60*0.984807753012)/(0.819152044289)`

`b=(59.08846518072)/(0.819152044289)`

`b=72.1336967815383509`

`b\approx 72`

Therefore, the measure of side 'b' is approximately 72 units.