Answer:
![B=36.87](https://img.qammunity.org/2021/formulas/mathematics/high-school/uyu6h0xd8o5zn51iutvqftbmver9jlsk5e.png)
Explanation:
As we are given the adjacent (a) side and the hypotenuse (h), we can use the cosine function to find the measure of angle B.
Recall that
![cos(B)=(a)/(h)](https://img.qammunity.org/2021/formulas/mathematics/high-school/rk6tqc3v50kb3yrqhat3dxrt5qkv9q01df.png)
This means that in order to find B, we need to take the inverse of cosine
This gives us
![B=cos^(-1) ((4)/(5) )](https://img.qammunity.org/2021/formulas/mathematics/high-school/vtf28zlb6lfpf6xl2gmq1rgsja1tgl1k35.png)
From a calculator, we find that the answer of this is
![B=36.869](https://img.qammunity.org/2021/formulas/mathematics/high-school/ju5seamvz9oyekye0ylt6fv2gjor8fm4ip.png)
When this is rounded to the nearest hundredth, we get
![B=36.87](https://img.qammunity.org/2021/formulas/mathematics/high-school/uyu6h0xd8o5zn51iutvqftbmver9jlsk5e.png)