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Answer:

The height of the cliff is 81.6m

Step-by-step explanation:

Please see the attachment below for an illustrative diagram representing the situation.

Step-by-step explanation:

From the diagram

x = /AB/

The height of the cliff is given by ( x + 1.6m)

Considering triangle ABC which is a right-angle triangle

/AB/ is the opposite and

/BC/ is the adjacent ; /BC/ = 50m

Angle of elevation is 58°

Then, we can write that

Hence, Side /AB/ = 80.0m

Since, /AB/ = x

∴ x = 80.0 m

Recall, the height of the cliff is given by

x + 1.6m

= 80.0m + 1.6m  

= 81.6 m

Hence, the height of the cliff is 81.6m

Answer:

80.02m

Step-by-step explanation:

Find the diagram attached. Using SOH, CAH, TOA to find the height of the cliff AC,

AC is the opposite side and BC is the adjacent

Given BC = 50m and ∠ABC = 58°

tan∠ABC = AC/BC

tan58° = AC/50

cross multiply

AC = 50tan58°

AC = 80.02m

Hence the height of the cliff is 80.02m

Answer: Choice B.

The statement is valid because the measure of the vertices located in the center of the pentagon is the quotient of 360 and 5, and the sum of two base angles in the given isosceles triangle is 108.

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Explanation:

Check out the diagram below. I have added x and y such that

x = base angle

y = vertex angle (located adjacent to center of polygon)

The pentagon is sliced up like a cake into 5 equal portions. Each vertex angle is y = 360/5 = 72 degrees.

The two base angles x must add with the vertex angle y to get 180

(angle1)+(angle2)+(angle3) = 180

x+x+y = 180

2x+y = 180

2x+72 = 180

2x = 180-72

2x = 108

This is true for any one of the five triangles. Notice that for angle LMN, we can divide it into LMQ and QMN where Q is the center of the polygon. Both of these angles are x. Since we've shown 2x = 108, we can see that LMN must also be 108 as well.

Choice A is close, but we wouldn't use the exterior angle theorem. Choice B is the better answer.

Answer:

Step-by-step explanation:

We have been given that the amount of a persons paycheck p varies directly with the numbers of hours worked t.

Since we know that the equation for direct variation is in form: , where, k represents the constant of variation.

We are also told that for 16 hours of work, the paycheck is $124.00. We can represent our given information as:

Upon substituting p=124 and t=16 in directly proportional equation we will get,

Let us divide both sides of our equation by 16 to solve for k.

Upon substituting the value of constant of variation in our equation we will get,

Therefore, the equation represents the relationship between hours of work and pay.