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2 years ago

Q5. At a certain time of day, a man 6 feet tall casts a shadow 4 feet in length. At the

Mathematics

1 answer:

nirvana33 [79]2 years ago

8 0

The height of the church steeple is 42 feet

<h3>How to determine how high, in feet, is the church steeple?</h3>

The given parameters are

Height of the man = 6 feet

Length of the man's shadow = 4 feet

Length of the shadow of the church steeple = 28 feet

To determine how high, in feet, is the church steeple, we use the following equivalent ratio:

Height of the man : Length of the man's shadow = Height of the church steeple: Length of the shadow of the church steeple

Substitute the known values in the above equation

6 feet : 4 feet = Height of the church steeple : 28 feet

Express the above equation as a fraction

6 feet/4 feet = Height of the church steeple/28 feet

Multiply both sides of the above equation by 28 feet

28 feet * 6 feet/4 feet = Height of the church steeple/28 feet * 28 feet

This gives

28 feet * 6 feet/4 feet = Height of the church steeple

Evaluate the product in the above equation

168 feet/4 = Height of the church steeple

Evaluate the quotient in the above equation

42 feet = Height of the church steeple

Rewrite as:

Height of the church steeple = 42 feet

Hence, the height of the church steeple is 42 feet

Read more about equivalent ratios at:

brainly.com/question/2328454

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A 15 ft ladder makes a 52° angle with the ground. How far will the top of the ladder be above the ground.

levacccp [35]

Answer:

11.820 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that ...

Sin = Opposite/Hypotenuse

The length of the ladder is the hypotenuse of a right triangle with 52° as the base angle. The side opposite is the height up the building where the top of the ladder rests. So, you have the relation ...

sin(52°) = height/(15 ft)

Multiplying by the denominator gives you ...

height = (15 ft)·sin(52°) ≈ 11.820 ft

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You may need to round this number appropriately.

5 0

4 years ago

A pile of earth removed from an excavation is a cone measuring 6ft high and 30ft across its base. How many trips will it take to

nignag [31]

Answer: 14

Step-by-step explanation:

Given

Excavation cone measures

height $h=6\ ft$

Diameter $d=30\ ft$

Truck can dump $125\ ft^3$ at a time

The volume of a cone is

$V=\dfrac{1}{3}\pi r^2h$

Putting values

$\Rightarrow V=\dfrac{1}{3}\times \pi\times 15^2\times 6\\\Rightarrow V=1413.9\approx 1414\ ft^3$

No of trips(N) required to accumulate this much volume is given by

$\Rightarrow N=\dfrac{1414}{125}=13.3\approx 14$

Therefore, 14 trips are necessary to accumulate a cone of volume $1414\ ft^3$

8 0

3 years ago

In this parallelogram. the measure of

balu736 [363]

Consecutive angles are supplementary (A + D = 180°). If one angle is right, then all angles are right. The diagonals of a parallelogram bisect each other. Each diagonal of a parallelogram separates it into two congruent triangles. A square has got 4 sides of equal length and 4 right angles (right angle = 90 degrees). Since ALL the angles in aquadrilateral add up to 360 then 360 divided by 4 must be 90.

4 0

3 years ago

A plane flying horizontally at an altitude of 3 miles and a speed of 500 mi/h passes directly over a radar station. Find the rat

konstantin123 [22]

Answer:

The rate at which the distance from the plane to the station is increasing is 331 miles per hour.

Step-by-step explanation:

We can find the rate at which the distance from the plane to the station is increasing by imaging the formation of a right triangle with the following dimensions:

a: is one side of the triangle = altitude of the plane = 3 miles

b: is the other side of the triangle = the distance traveled by the plane when it is 4 miles away from the station and an altitude of 3 miles

h: is the hypotenuse of the triangle = distance between the plane and the station = 4 miles

First, we need to find b:

$a^{2} + b^{2} = h^{2}$ (1)