Question

Need to study for finals need help on this problem on my study guide find the measure of each angle calculate the length of each side

Answer 1

`\begin{gathered} m\angle B\text{ = 28}\degree \\ AB\text{ = 9.75} \\ BC\text{ = 7.7} \end{gathered}`

Step-by-step explanation:

Here, we want to calculate the measure of each of the missing angles and sides

We have one missing angle and 2 missing sides

a) Let us get the angle at B

Mathematically, the sum of angles in a triangle is 180 degrees

Thus:

`\begin{gathered} 90\text{ + 62 + B = 180} \\ B\text{ = 180-90-62} \\ B\text{ = 28}\degree \end{gathered}`

b) Let us get the measure of AB

We can use the appropriate trigonometric ratio here

The side that measures 6 is an opposite to the angle B

Since AB is the hypotenuse (the side facing the right angle and the longest side of in the triangle), we use sine

Sine is the ratio of the opposite and the hypotenuse

Mathematically:

`\begin{gathered} sin\text{ 38 = }(6)/(AB) \\ \\ AB\text{ =}\frac{6}{sin\text{ 38}} \\ \\ AB\text{ = 9.75} \end{gathered}`

c) side BC

We can use tan to get this

Tan is the ratio of the opposite to the adjacent side

The opposite side here is the side AC, while the adjacent is BC

Thus, we have it that:

`\begin{gathered} Tan\text{ 38 = }(6)/(BC) \\ \\ BC\text{ = }\frac{6}{Tan\text{ 38}} \\ \\ BC\text{ = 7.7} \end{gathered}`