91Ó°ÊÓ

An observer on the roof of building \(A\) measures a \(27^{\circ}\) angle of depression between the horizontal and the base of building \(B\). The angle of elevation from the same point to the roof of the second building is \(41.42^{\circ} .\) What is the height of building \(B\) if the height of building \(A\) is \(150 \mathrm{ft}\) ? Assume buildings \(A\) and \(B\) are on the same horizontal plane.

Use the Law of Sines to solve the triangle. $$ \alpha=80^{\circ}, \beta=20^{\circ}, b=7 $$

Sketch the given vector. Find the magnitude and the smallest positive direction angle of each vector. $$ -4 \mathbf{i}+4 \sqrt{3} \mathbf{j} $$

Sketch the given vector. Find the magnitude and the smallest positive direction angle of each vector. $$ \mathbf{i}-\mathbf{j} $$

Use the Law of Cosines to solve the triangle. $$ a=7, b=9, c=4 $$

Use the Law of Sines to solve the triangle. $$ \alpha=80^{\circ}, \beta=20^{\circ}, b=7 $$

The top of a 20 -ft ladder is leaning against the edge of the roof of a house. If the angle of inclination of the ladder from the horizontal is \(51^{\circ}\), what is the approximate height of the house and how far is the bottom of the ladder from the base of the house?

Use the Law of Sines to solve the triangle. $$ \beta=37^{\circ}, \gamma=51^{\circ}, a=5 $$

Sketch the given vector. Find the magnitude and the smallest positive direction angle of each vector. $$ -10 \mathbf{i}+10 \mathbf{j} $$

Use the Law of Cosines to solve the triangle. $$ a=11, b=9 \cdot 5, c=8.2 $$