Questions: Use a calculator to find the length of each side to four decimal places. a= b= Enter a number.

Solution Steps

We are given a right triangle with:

• One leg (adjacent to the 65° angle) = 24 units
• One angle = 65°
• The right angle = 90°

To find the length of side 'a' (opposite to the 65° angle), we use the tangent function: \[ \tan(65°) = \frac{a}{24} \] \[ a = 24 \times \tan(65°) \]

Using a calculator: \[ \tan(65°) \approx 2.1445 \] \[ a = 24 \times 2.1445 \approx 51.468 \]

To find the length of side 'b' (the hypotenuse), we use the cosine function: \[ \cos(65°) = \frac{24}{b} \] \[ b = \frac{24}{\cos(65°)} \]

Using a calculator: \[ \cos(65°) \approx 0.4226 \] \[ b = \frac{24}{0.4226} \approx 56.787 \]

Final Answer