SOLUTION: Land in the shape of an isosceles triangle has a base of 130 m. An altitude from one of the legs of the triangle is 120 m. What is the area of the property? These are the possible

Algebra ->  Surface-area -> SOLUTION: Land in the shape of an isosceles triangle has a base of 130 m. An altitude from one of the legs of the triangle is 120 m. What is the area of the property? These are the possible      Log On


   

Question 936210: Land in the shape of an isosceles triangle has a base of 130 m. An altitude from one of the legs of the triangle is 120 m. What is the area of the property?
These are the possible answers.
A)3000 B)9840 C)9512 D)10140 E)10200
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let your triangle be ABC.

draw it so that A is on the bottom left and C is on the bottom right and B is in the top middle.

let AB be the leg that is 130 cm.

this means that BC and AC are the equal legs of the isosceles triangle.

draw a perpendicular from B to intersect with AC at D.

BD becomes the height of the triangle and AC becomes the base of the triangle for purposes of calculating the area of the triangle.

you are told that the length of BD is equal to 120 cm, because BD is the altitude of the triangle and the altitude of the triangle is the same thing as the height of the triangle.

you need to find the length of AC.

this is because the area of the triangle is equal to 1/2 * the height * the base which becomes 1/2 * BD * AC.

you can use trigonometry to help you find the length of AC.

BD breaks AC into two parts.
one of them is AD which is part of right triangle ABD.
the other of them is BC which is part of right triangle CBD.

sin(A) is equal to opposite / hypotenuse which is equal to BD / AB which is equal to 120/130.

arcsine(120/130) = 67.38... degrees, therefore angle A is equal to 67.38... degrees.

since the base angles of an isosceles triangle are equal, this means that angle B is also equal to 67.38... degrees.

this means that angle C must be equal to 180 - 2 * 67.38... degrees which makes angle C equal to 45.2397... degrees.

sin(C) = BD/BC

this becomes:

sin(45.2397...) = 120 / BC

solve for BC to get:

BC = 120 / sin(45.2397...) which becomes:

BC = 169.

since AC and BC are of equal length, this means that AC also has a length of 169.

you now know the height and the base of the triangle for calculation of area purposes.

the height is 120.
the base is 169.

the area is equal to 1/2 * 120 * 169 which is equal to 10140.

i believe that's one of your selections.

a picture of your triangle is shown below:

$$$