The angle of elevation of a building 80 m high from a man on the ground is 50.41 degrees. How far is the man from the building?

Question: The angle of elevation of a building 80 m high from a man on the ground is 50.41 degrees. How far is the man from the building?

Solution:

This is a very simple trigonometry question. The ground, the building, and the angle of elevation represent a right angle triangle with an angle α of 50.41° between the hypotenuse(The line of sight from the man’s eye to the top of the building) and the ground. The tangent of this angle is the opposite which is the building elevation of 80m divided by the adjacent which is the unknown horizontal distance between the man and the building. This distance denoted by X is what we are looking to determine.

In math form, we have the equation tanα = 80 m / X and X (tanα) = 80m divide by tanα

X = 80m / tanα = 80m / tan 50.41° = 66.2 m

The sum of two numbers is 46. When 30 is subtracted from 5 times the smaller the result is 3 times the larger.

The sum of two numbers is 46. When 30 is subtracted from 5 times the smaller the result is 3 times the larger. Determine the numbers.

ANSWER:

Let x be the smaller number and y be the larger number.

equation 1: x + y = 46 —>—->—->—-> y = 46 – x
equation 2: 5x – 30 = 3y

sub (equation 1) in (equation 2);
5x – 30 = 3y y= 46 -x
5x – 30 = 3( 46 – x) y = 46 – 21
5x – 30 = 138 – 3x y = 25
-30 – 138 = -3x – 5x
-168 = -8x
x = 21

.*. The smaller number is 21 and the larger number is 25

A play needs three protagonists (a man, a woman, and a girl), two antagonists (a man and a woman), and two supporting roles (a man and a boy).

A play needs three protagonists (a man, a woman, and a girl), two antagonists (a man and a woman), and two supporting roles (a man and a boy).

Six men, six women, three boys, and four girls attended the auditions. The number of ways the roles can be cast is:

ANSWER:

woman can be protagonists or antagonists

six women are there

2 women can be selected in ⁶C₂ = 15 ways and can be assigned role in 2! = 2 ways

Hence total ways role to woman can be assigned = 15 x 2 = 30

Man can be protagonists , antagonists , supporting role

six men are there

3 men can be selected in ⁶C₃ =20 ways and can be assigned role in 3! = 6 ways

Hence total ways role to woman can be assigned =20 x 6 = 120

Girl can be protagonists

There are 4 girls

Hence 4 ways

Boy can be supporting roles

There are 3 boys

Hence 3 ways

Total Ways = 30 x 120 x 4 x 3

= 43,200

The number of ways the roles can be cast is: 43200

For lines a, c, and d, line c is parallel to line d and m∠1 = 55°. : For the

For lines a, c, and d, line c is parallel to line d and m∠1 = 55°.

: For the given diagram, use the measure of ∠1 to find the measure of the remaining seven angles.
: In two or more complete sentences, explain the relationship between angle pairs a)∠1 and ∠7 and b)∠1 and ∠2. in your explanation, include how you calculated each of the angle measures in the special angle pairs.