Given that 4x – 5y = 21

1 answer:

7 0

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ABCD diagonals intersect at E. If m∠BAC=4x+5 and m∠CAD=5x-14, then find m∠CAD.

Travka [436]

Answer: m∠CAD = 81°

Step-by-step explanation: Diagonal is a line that unites opposite sides.

ABCD is a prallelogram. One property of diagonal in a parallelogram is it separates the parallelogram in 2 congruent triangles.

The figure below shows ABCD with its diagonals.

Since diagonal divides a parallelogram in 2 congruent triangles, it means the internal angles are also congruent. So

m∠BAC = m∠CAD

4x + 5 = 5x - 14

x = 19

Then, m∠CAD is

m∠CAD = 5(19) - 14

m∠CAD = 81

The angle m∠CAD is 81°.

7 0

3 years ago

A statue is mounted on top of a 16 foot hill. From the base of the hill to where you are standing is 77 feet and the statue subt

DanielleElmas [232]

Consider right triangle with vertices B - base of the hill, S - top of the statue and Y - you. In this triangle angle B is right and angle Y is 13.2°. If h is a height of the statue, then the legs YB and BS have lengths 77 ft and 16+h ft.

You have lengths of two legs and measure of one acute angle, then you can use tangent to find h:

$\tan 13.2^{\circ}=\dfrac{\text{opposite leg}}{\text{adjacent leg}} =\dfrac{16+h}{77}, \\ \\ 0.2345=\dfrac{16+h}{77},\\ \\ 16+h=0.2345\cdot 77=18.0565,\\ h=18.0565-16=2.0565$ ft.