find angle and sides of triangle

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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The problem provides the information that the angles made by both sides to the base of 44 are equal, hence the triangle is isosceles and the sides that make equal angles to the base are equal.

You need to use the law of cosine to find the angle `theta`  and the side c.

`c^2 = c^2 + 44^2 - 2*44*c*cos theta`

Reducing like terms yields:

`2*44*c*cos theta = 44^2`

Reducing by 44 both sides yields:

`2*c*cos theta = 44 =gt c*cos theta = 22 =gt cos theta = 22/(cos theta)`

You notice that inside triangle there is one small right triangle whose legs are of 6 ft and 11 ft.

You may find the measure of angle `theta`  using trigonometric functions. Since you know the legs, you should use tangent function, hence:

`tan theta = (6 ft)/(11 ft) =gt theta ~~ 29^o`

You may find the length of side c such that:

`c = 22/(cos theta) =gt 22/0.874 =gt c = 25.17 ft`

Hence, evaluating the side c and the angle theta of triangle yields`c = 25.17`  ft and `theta ~~ 29^o` .

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