trapped in trig!!?

Question

*if an iscoseles triangles legs are 32 each..whats the hypotenuse?
*the hypotenuse of an iscoseles right triangle is 8.2 in. long what is the length of each leg? (in formula form)
*a lddaer 12m long that leans against a building makes an angle of 60 degrees w/ the ground how far up the wall does it reach?


i seriously cant get it, im trying my hardest to get it and keep telling myself i can but its not coming through
and just so you know, im in 7th grade...honors...i cant quite keep up so at the risk of sounding stupid i plead for help here!!

Answer 1

Using the Pythagorean theorem:

c^2 = a^2 + b^2 where:

c = Hypotenuse
a = One leg of the right triangle (either adjacent or opposite)
b = Another leg of the triangle (either adjacent or opposite)

Now you have 32 for the adjacent the opposite legs and you want to find C in the above formula

c^2 = 32^2 + 32^2 = 1024 + 1024 = 2048
c = Sqrt(2048) = 45.2548

I will leave the rest up to you.
Good luck.

Answer 2

Pythagorus tells us that for an isoceles right triangle, the sides are in the ratio 1,1, sqrt (2). This can be recast so if you know the hypotenuse, the sides are 1/2 the hypotenuse x sqrt (2).
As we all know (DONT WE!!) sqrt(2) = 1.414

The first problem is missing something. If the isosceles triangle is also a right triangle, the hypotenuse is 32 sqrt(2) .

In the second, you have the reverse situation- you know the hypotenuse but not the two sides (which are equal). So the side would be 4.1 sqrt(2) = whatever.

The last problem is a 30/60/90 right triangle setup. Here, the 3 sides are in the ratio of
1 (small side)
sqrt(3) (larger side)
2 (hypotenuse)
In this problem, the hypotenuse is the 12 m lenght of the ladder (that's a biggie). The ladder will go up the wall 6 sqrt(3) meters, or appx 10.4 meters. You can set up a proportion to solve this. large side/hypotenuse= sqrt(3)/2 = x/12

Hang in there, 7th grade anything is a real hassle.

Answer 3

Don't panic!

OK, since you're calling the third side of the isosceles triangle a hypotenuse then I'll assume it's a right-angle isosceles triangle. In this case you can use the Pythagorean theorem: 32^2 + 32^2 = h^2; 128 = h^2;
h^2 = 2048; h = saqrt(2048) =

For the second one you just reverse the process:

8.2^2 = s^2 + s^2; 67.24 = 2s^2; s^2=33.62; s= sqrt(33.62)

For the last one, you know the angle is 60 degrees; so the sine of the angle = opposite/hypotenuse, so

sin(60)=x/12;
0.866=x/12; x = 0.866*12 = 10.4

Answer 4

-for the ladder problem the length of the ladder is the hypotenuse and it forms a right angle with the floor and wall. So you have a 30,60,90 triangle.
for 1 and two im not sure, but try setting up an equation. Divide the triangle in 1/2 so you have two righ triangles with one side 32. Then since you know the two triangles re congruent and the sum of all degrees will equal to 180, you can set two equations equal to eachother.

Answer 5

Use the Pythagorean Theorem. It's not as hard as you think it is. a, b, and c all equal the three sides of the triangle. Because it's an iscoseles triangle, you know that two of the sides are equal.
Pythagorean Theorem is a²+b²=c². . . 32²+32²= c²
Therefore, 1024+1024= c², c²=2048. c = the square root of 2048, which equals about 45.
Try this website if you need more help:
http://planetmath.org/encyclopedia/Triangle.html

Answer 6

good question for a 7th grader. 10th graders I teach don't always get these.

Remember a^2 + b^2 = c^2 ALWAYS, and when the triangle is iscosoles, a = b.

so in that case 2 * a^2 = c^2. go from there