Question

Could you help me with these problems ? I don't really know how to put the equation together and the steps I should take to solve it, it would be amazing if you could show me how, and I'd be very thankful if you could also add a picture showing the steps if possible. Thank you so much.

Answer 1

Since it is a right triangle, you can use the trigonometric ratio sin(θ) to solve the exercise:

`\sin (\theta)=\frac{\text{opposite side}}{\text{hypotenuse}}`

Graphically,

So, in this case, you have

`\begin{gathered} \theta=54\text{\degree} \\ \text{ Opposite side }=72 \\ \text{ Hypotenuse }=x \\ \sin (54\text{\degree})=(72)/(x) \\ \text{ Multiply by x from both sides of the equation} \\ \sin (54\text{\degree})\cdot x=(72)/(x)\cdot x \\ \sin (54\text{\degree})\cdot x=72 \\ \text{ Divide by }\sin (54\text{\degree})\text{ from both sides of the equation} \\ \frac{\sin(54\text{\degree})\cdot x}{\sin(54\text{\degree})}=\frac{72}{\sin(54\text{\degree})} \\ x=\frac{72}{\sin(54\text{\degree})} \\ x=(72)/(0.8090) \\ x=88.99 \\ \text{ Rounding to the nearest tenth} \\ x=89.0 \end{gathered}`

Therefore, the measure of the missing side is 89.