A curtain on the window was tied at the bottom part forming an inverted isosceles triangle. The angle at the vertex located in the tied part is 40 deg and its opposite side is 4 ft. Find the length of the remaining sides'

1
by xedterdj

• Brainly User
2016-03-11T22:33:34+08:00

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Solve the measure of remaining sides using Law of Sines:

Given:
Vertex angle = 40 degrees
Opposite side of vertex  (base)= 4 ft.
Base angle = 70 degrees
Opposite side of base angle (leg) = x

Note: Base angle = (180° - 40°)/2
= 140° - 2
= 70°

Solution:

4 ft                x
------------   =  ---------
sin 40°          sin 70°

x (sin 40°)  =  4 ft (sin 70°)

x (sin 40°)      4 ft (sin 70°)
---------------- =  ------------------
( sin 40°)          (sin 40°)

4 ft (0.9377)
x = --------------------
0.6428

3.7588 ft.
x = -------------
0.6428

x = 5.85 ft or 6 ft.

ANSWER:  The remaining sides are 6 ft each in measure because legs of an isosceles triangle are congruent.