Question

application: 14 marks

1. angle a is between 0° and 180°. determine all measures of angle a if sin a = 0.4432. (round to 1 decimal place)

4 marks

1. mario has to save princess peach, who is locked in a tower. he takes a ladder that is 20 meters long and leans it against the tower at an angle of 65° with the ground. the ladder reaches just to princess peachs window. what is the height of the window? include a concluding sentence at the end and round to 1 decimal place.

4 marks

Explanation:

Step1: Use the sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, the hypotenuse (length of the ladder) \(c = 20\) meters and the angle with the ground \(\theta=65^{\circ}\), and we want to find the height \(h\) (opposite side to the angle \(\theta\)). So, \(h = 20\times\sin(65^{\circ})\).

Step2: Calculate the value of \(\sin(65^{\circ})\)

We know that \(\sin(65^{\circ})\approx0.9063\). Then \(h = 20\times0.9063=18.126\).

Step3: Round the result

Rounding \(18.126\) to \(1\) decimal place, we get \(h\approx18.1\) meters.

Answer:

The height of the window is approximately \(18.1\) meters.