Question

q30. a ladder is placed against a building. if the ladder makes a 55° angle with the ground, what is the measure of the angle that the ladder makes with the building? a. 35° b. 40° c. 55° d. 90° answer _

Explanation:

Step1: Recall the property of angles in a right - triangle

The sum of angles in a triangle is \(180^{\circ}\). When a ladder is placed against a building, the ground, the building and the ladder form a right - triangle (assuming the building is perpendicular to the ground, so one angle is \(90^{\circ}\)). Let the angle with the ground be \(\theta = 55^{\circ}\), the right - angle is \(90^{\circ}\), and the angle with the building be \(\alpha\).

Step2: Use the angle - sum formula for a triangle

We know that for a triangle with angles \(A\), \(B\), and \(C\), \(A + B+C=180^{\circ}\). In our right - triangle, if \(A = 90^{\circ}\), \(B = 55^{\circ}\), and \(C\) is the angle with the building. Then \(C=180^{\circ}-(90^{\circ}+ 55^{\circ})\).

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Answer:

A. \(35^{\circ}\)