# I'm so confused with this math question-i'm terrible at math?

Two buildings are 35m apart. From the top of the shorter building, the

angle of depression to the base of the other is 47° and the angle of

elevation to the top of it is 21°. Find the height of the taller

building.

Relevance
• What King Leo said.

• Hint:

draw a diagram

use SOH , CAH or TOA

• Let R be a line from the top of the shorter to the base of the taller:

90° - 47° = 43°

R = 35/sin43 = 51.32 = 35/cos47

Hs = R*sin47 = 51.32*sin47 = 37.53m height of the short building

Hd = 35*tan21 = 13.44m the amount taller

So the taller building is 37.53+13.44 = 50.97 or about 51m

• .

Height of tall building

= 35 tan(21°) + 35 tan(47°)

= 50.97 m

———— — • Draw it out You have a triangle with an altitude of 35 meters. The side opposite of the observer can be broken into 2 segments, a and b. Using the law of sines, we can find their lengths

sin(47) / a = sin(90 - 47) / 35

sin(47) / a = cos(47) / 35

35 * sin(47) = a * cos(47)

35 * tan(47) = a

sin(21) / b = sin(90 - 21) / 35

35 * sin(21) = b * cos(21)

35 * tan(21) = b

35 * tan(47) + 35 * tan(21) =>

35 * (tan(47) + tan(21))

Make sure that your calculator is in degree mode

50.968146077103441512111665466154

To 2 sf

51 m

• First, draw a pic

use SOHCAHTOA since you have right triangles.

• Often, it's a matter of envisioning the problem, especially this kind.

So, sketch the givens:

--- draw the ground (horizontal line on the page)

--- draw a vertical line for the short building (perpendicular to the ground line

--- draw a vertical line for the taller building.

--- draw a line perpendicular to the taller line to the "top" of the shorter building

--- draw a line from the top of the shorter building to the top of the other one

--- draw a line to the top of the shorter building to the bottom of the other

Now, put in the numbers that you know:

the ground between the buildings is 35 metres So two lines have this length.

the angle between the line across from the shorter building and the line to the top of the taller building is 21 degrees, and the line to the bottom of the taller building is 47 degrees.

Now use what you know of trigonometry, geometry and algebra.

Let h be the height of the taller building

and x be the height of the shorter building

so tan(21) = (h-x)/35

==> h-x = 35tan(21)

and tan(47) = x/35

==> x = 35tan(47)

you have two equations:

and you get:

h = 35tan(21) + 35tan(47) = 35 (tan(21) + tan(47))

look up tan(21) and tan(47) (or use your calculator)

and do the arithmetic

and you have the right answer

• That is a simple Right Triangle problem. Actually Two Right Triangles.

You solve the Triangle for the smaller one first then that will give you the numbers you need for the larger one.

• Draw out a picture. Remember that tan() = opposite/adjacent

Tan(47°) = x/35

35 tan(47°) = x

x = 37.53 m << this is the height of the shorter building

tan(21°) = y/35

35 tan(21°) = y

y = 13.44 m << this is how much higher that tall building is over the shorter building

So height of taller building is x + y = 37.53 + 13.44 = 50.97 m

To use the right number of sig figs, height of taller building is 51 meters.

• Draw it out on graph paper. Use trig functions for angles measured from verticals and horizontals