Anonymous
Anonymous asked in Science & MathematicsMathematics · 3 weeks ago

# can someone please answer both or 1 of these questions, thx!?

At night, a security camera pans over a parking lot. The camera is on

a post at point A, which is 35m from point C and 51m from point B. The

distance from B to C is 65m. Calculate ∠A, the angle through which the camera

pans, correct to the nearest degree.

Micah is standing on the ground between two buildings on the opposite sides of

a park. The base of the first building is 152 m from Micah, has an angle of

elevation of 38° to the top, while the base of the second building is 175 m from

Micah, and hast an angle of elevation of 53° to the top. How far apart are the

tops of the two buildings? Round your answer to the nearest meter.

Relevance

(1)

It doesn't explicitly state, but assuming the camera pans from B to C.

The Law of Cosines:

a² = b² + c² − 2bc cos(A)

cos(A) = (-a² + b² + c²) / 2bc

cos(A) = (-65² + 35² + 51²) / 2(35)(51)

A = 96°

(2)

Height of Bldg 1 = 152•tan38°

= 118.7m

Height of Bldg 2 = 175•tan53°

= 232.2m

Difference in heights = 232.2 - 118.7 = 113.5m

The diagonal from rooftop 1 to rooftop 2:

d = √((152 + 175)² + 113.5²)

d = 346m

• Sketching it out we get a triangle with three known lengths and no known angles.  You want the measurement of angle "A", so we use its opposite length of 65 m in the law of cosines equation:

a² = b² + c² - 2bc cos(A)

65² = 35² + 51² - 2(35)(51) cos(A)

4225 = 1225 + 2601 - 3570 cos(A)

4225 = 3826 - 3570 cos(A)

399 = -3570 cos(A)

-399/3570 = cos(A)

A ≈ 96° (rounded to the nearest whole degree)