SOLUTION: The petronas Tower 2 in Kuala Lumpur ,Malaysia, is one of the tallest buildings in the world. from a position x on level ground, the angle of elevation to the top is 80 degrees. P

Question 233471: The petronas Tower 2 in Kuala Lumpur ,Malaysia, is one of the tallest buildings in the world. from a position x on level ground, the angle of elevation to the top is 80 degrees. Position Y is lies 84.81m further back from x in a direct line with the building. The angle of elevation from Y to the 70 degrees. How high is the Petronas Tower 2?
Please help me solve this question. This is extremely difficult for me.
Thankyou very much indeed.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
Kuala Lumpur Tower can be seen by clicking on the Tower Hyperlink.

There are twin towers connected by a walkway about halfway up.

The height is 451.9 meters which includes the spires.

The other pertinent facts are that the roof is 378.6 meters high, while the top floor is 375 meters high.

What you will be looking for is an answer that is 451.9 meters high.

Fortunately, it's been found as follows:

You are given that the angle from the street level to the top of the tower is 80 degrees from point x.
You are also given that the angle from the street level to the top of the tower is 70 degrees from point y.

The distance from the base of the tower to point x is unknown.

We'll call it a.

The distance from point x to point y is 84.81 meters.

We'll call it b for now, and substitute the actual number for b later.

This makes the distance from the base of the tower to point y equal to (a + b)

We'll call the height of the tower c.

We have:

c = height of the tower.
a = distance from the base of the tower to x.
a + b = distance from the base of the tower to y.
angle between the street and the top of the tower at point x = 80 degrees.
angle between the street and the top of the tower at point y = 70 degrees.

The formula we will be using is the tangent formula.

tangent (angle) = opposite side / adjacent side.

from point x, tan(80) = c/a

from point y, tan(70) = c/(a+b)

If we solve for c in both equations, we get:

c = a * tan(80)
and:
c = (a+b) * tan(70)

Since both these equations equal to c, then they are equal to each other, so we get:

a * tan(80) = (a + b) * tan(70)

We remove parentheses on the right side of the equation to get:

a * tan(80) = a * tan(70) + b * tan(70)

We subtract a * tan(70) from both sides of the equation to get:

a * tan(80) - a * tan(70) = b * tan (70)

We factor out the a on the left side of the equation to get:

a * (tan(80) - tan(70)) = b*tan(70)

we divide both sides of this equation by (tan(80)-tan(70)) to get:

a = b*tan(70) / (tan(80) - tan(70))

We replace b with the value of b to get:

a = (84.81*tan(70)) / (tan(80)-tan(70))

After we do the arithmetic, this becomes:

a = 79.69533117

Since we know that:

c = a * tan(80), then we can now solve for c to get:

c = 79.69543117 * 5.67128182 = 451.9746828 meters.

If you care to do the calculations yourself, the pertinent missing facts are:

tan(70) = 2.747477419
tan(80) = 5.67128182
tan(80) - tan(70) = 2.9238044

RELATED QUESTIONS
At a height of 1483 ft, the Petronas Towers in Kuala Lumpur, Malaysia, is one of the... (answered by Alan3354)

At a height of 1483 ft, the Petronas Towers in Kuala Lumpur, Malaysia, is one of the... (answered by Alan3354)

ALAN3354 - please do not respond...I have never received anything but harassment from... (answered by Alan3354)

At a height of 1483 ft, the Petronas Towers in Kuala Lumpur, Malaysia, is one of the... (answered by macston)

Please help me solve this word problem: Two of the tallest buildings in the world are... (answered by CubeyThePenguin)

An object is dropped from 39 feet below the tip of the pinnacle atop one of the... (answered by Alan3354)

The Petronas Towers in Kuala Lumpur, Malaysia, are the world’s tallest twin towers.... (answered by ankor@dixie-net.com)

The Petronas Towers in Kuala Lumpur, Malaysia, are the world's tallest twin towers. Each... (answered by Theo)

How can I solve the following problem: The tallest inhabited building in the world is the (answered by Earlsdon)