It appears that when we have SSA, we could end up with 0, 1, or 2 triangles! Under what circumstances will we end up with:

2 triangles

1 triangle

0 triangles

Law of Sines

Impossible

What if B is a right angle?

2 triangles

1 triangle

0 triangles

Law of Sines

Impossible

What if B is an obtuse angle?

2 triangles

1 triangle

0 triangles

Law of Sines

How does the Law of Sines give us results that are consistent with the geometric results?

Law of Sines

b. Approximate the height of the mountain.

a. Approximate the distance between A and P.

A cable car carries passengers from a point A, which is 1.2 miles from point B at the base of a mountain to a point P at the top of the

mountain. The angles of elevation of P from A and B are 21° and 65°, respectively.

1.57 mi

0.56 mi

A solar panel 10 feet in width is to be attached to to a roof that makes an angle of 25° with the horizontal. Approximate the

length d of the brace that is needed for the panel to make an angle of 45° with the horizontal. 3.77 ft

A helicoptor hovers at an altitude that is 1000 feet above a mountain peak of altitude 5210 feet, as shown in the figure. A second, taller peak is viewed from both the mountaintop and the helicoptor. From

the helicoptor, the angle of depression is 43°, and from the mountaintop, the angle of elevation is 18°.a. Approximate the distance

from peak to peak.

b. Approximate the altitude of the taller peak.

836 ft

5468 ft