Mathematics: Parallelogram PQRS has diagonals PR and SQ that intersect at T. Given SP=2a+5, RQ=5a−1, ST=3b−3, and SQ=7b−9, what are the values of RQ and TQ?

Parallelogram PQRS has diagonals PR and SQ that intersect

Ответ:

danteyoungblood7

27.06.2020

Mathematics

Approximately, there is a distance of 25,6 foot between the base of the flagpole to the house.

Step-by-step explanation:

We are given the following in the question:

Height of pole = 20 foot

Angle between pole and ground = 85 degrees

Angle of elevation from the base of the house to the top of the pole = 55 degrees

Then, the third angle of the triangle can be found as:

Angle sum property of triangle: The sum of the three angles of a triangle is 180 degrees.

$x + 85 + 55 = 180\\x = 180 - 140\\x = 40^\circ$

Thus, by the sin rule, we can write:

$\dfrac{\text{Distance from the base of the flagpole to the house}}{\sin 55} = \dfrac{20}{\sin 40}\\\\\Rightarrow \text{Distance from the base of the flagpole to the house} = 20\times \dfrac{\sin 55}{\sin 40}\\\\=20\times \dfrac{0.82}{0.64} = 25.625$

Approximately, there is a distance of 25,6 foot between the base of the flagpole to the house.

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Parallelogram PQRS has diagonals PR and SQ that intersect at T. Given SP=2a+5, RQ=5a−1, ST=3b−3, and SQ=7b−9, what are the values of RQ and TQ?

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