Question

inverse cosine quick check tammy is an electrician. when using a ladder, her company requires the angle formed between the ground and the ladder to be within 3° of 75°, so that she remains safe. if she is using a 20 - foot ladder and places the ladder 5 feet from the wall, is this within safety protocol? what is the approximate angle formed between the ground and the ladder? (1 point) no, the angle formed is approximately 90°. no, the angle formed is approximately 14°. yes, the angle formed is approximately 73°. yes, the angle formed is approximately 76°.

Explanation:

Step1: Identify the triangle type

We have a right triangle where the ladder is the hypotenuse (\( c = 20 \) feet), the distance from the wall is the adjacent side to the angle we want to find (\( a = 5 \) feet), and we can use the cosine function: \( \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{a}{c} \)

Step2: Calculate the cosine of the angle

Substitute \( a = 5 \) and \( c = 20 \) into the formula: \( \cos(\theta)=\frac{5}{20}=\frac{1}{4} = 0.25 \)

Step3: Find the angle using inverse cosine

\( \theta=\cos^{-1}(0.25) \). Using a calculator, \( \cos^{-1}(0.25)\approx75.52^{\circ}\approx76^{\circ} \)

Step4: Compare with the safe angle range

The safe angle range is within \( 3^{\circ} \) of \( 75^{\circ} \), so \( 75 - 3=72^{\circ} \) to \( 75 + 3 = 78^{\circ} \). Since \( 76^{\circ} \) is within this range, the angle is approximately \( 76^{\circ} \) and it is safe.

Answer:

Yes, the angle formed is approximately \( 76^{\circ} \) (the corresponding option: "Yes, the angle formed is approximately 76°")