Question

Please see image i would like some help with this problem!

Answer 1

Given,

The measure of the base of the right angles triangle is 21 unit.

The measure of the hypotenuse of the right angles triangle is 29 unit.

The pythagorean theorem states that the sum of the square of base and perpendicular of the right angles triangle is equal to the square of its hypotenuse.

`\text{hypotenuse}^2=\text{base}^2+\text{perpendicular}^2`

Substituting the values then,

`\begin{gathered} \text{29}^2=\text{21}^2+\text{perpendicular}^2 \\ 841-441=\text{perpendicular}^2 \\ \text{perpendicular}^2=400 \\ \text{perpendicular}^{}=20 \end{gathered}`

Hence, the measure of the missing side of the triangle is 20 unit.

The measure of the angle theta is,

`\begin{gathered} \tan \theta=(perpendicular)/(base) \\ \tan \theta=(20)/(21) \\ \theta=\tan ^(-1)((20)/(21)) \\ \theta=43.60^(\circ) \end{gathered}`

Hence, the measure of the theta is 43.60 degree (approximately)