Question

1. in right triangle ( abc ), hypotenuse ( ab = 15 ) and ( angle a = 35^circ ). what is ( bc )?

a quad 9.6
b quad 6.6
c quad 8.6
d quad 7.6

Explanation:

Step1: Identify the trigonometric ratio

In right triangle \(ABC\), \(\angle A = 35^\circ\), hypotenuse \(AB = 15\), and we need to find \(BC\). Let's assume \(\angle C = 90^\circ\) (since it's a right triangle). Then \(BC\) is the side opposite \(\angle A\), and \(AB\) is the hypotenuse. The sine of an angle in a right triangle is defined as \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\). So, \(\sin(\angle A)=\frac{BC}{AB}\).

Step2: Substitute the known values

We know that \(\angle A = 35^\circ\) and \(AB = 15\). Substituting these values into the sine formula, we get \(\sin(35^\circ)=\frac{BC}{15}\).

Step3: Solve for \(BC\)

To find \(BC\), we can multiply both sides of the equation by \(15\): \(BC = 15\times\sin(35^\circ)\). Using a calculator to find \(\sin(35^\circ)\approx0.5736\), then \(BC\approx15\times0.5736 = 8.604\approx8.6\).

Answer:

c. 8.6