Please help trig question

[Zahta]

a gardem bed is in the shape of a triangle, with sides of length 4m, 5.2m and 7m. The volume of topsoil needed to cover the garden to a depth of 250mm is


please help thanks

[MathsBoy1995]

2.57m^3

[Zahta]

the answer is 2.57 m^3

And why did you do that pleasse explain plus its wrong

[b^3]

Use heron's formula to find the area of the triangle. s=(4+5.2+7)/2 then area=root((s-4)*(s-5.2)*(s-7))
Then Volume=cross section area*height
=area above*.025 (in m^3)

[Zahta]

thankyou so much , also can you help me with this question .

A stepladder stands on a floor with its feet 2.18m apart. if the angle formed by the legs is 50 degress ,how high above the floor is to the top ladder

[b^3]

You have a triangle like this.
                       /\
                      /  \
                     /    \
                    /      \
                   /        \
I'm going to interpret the angle to be inbeween at the top/
Now split it into two so that You have a right angle
                       /|\
                      / | \
                     /  |  \
                    /   |   \
                   /    |    \
So now you have an angle of 25 degrees at the top and the base length is 1.14m.
                       /|
                      / |
                     /  |     h
                    /   |
                   /    |
                     1.14
So next trig ratios. tan(theta)=o/a=1.14/h, h=1.14/tan(25)

[Zahta]

okay thanks and one more question what was the point of finding the area and using herones formula i know you use herons formula when you have three sides and no angle but does that mean i have to find height and what do you mean cross section area *height .Confused Sorry

[Zahta]

and for the stepladder i get all of it but how did you get 1.14  shouldnt u do 2.18 divide by 2 because ders to bases now .

[b^3]

You have a flat triangle which you found the area of. I.e the area of the base (or what it's sitting on). If the shape is the same shape all the way up then this base area is equal to the cross-sectional area. So Volume=this area* how many units up this area goes.

I hope that makes sense.

For the other one, yes divide by two, thats what I meant, it was supposed to be 1.09 - my mistake, I'm a bit tired.

[Zahta]

yes it does make sense , thankyou so much i really appreciate it .

[Zahta]

hey can you help me with a question it says

A four wheel drive vehcile leaves a camp site and travels across a flat sandy plain in a direction of S65S m for a distance of 8.2 km. It then heads due south for 6.7km to reach a waterhole.

A) How far is the water hole from a camp site?

I did the question i drew  it and then i did the angle which 180-65 which is 115, and then used the cose rule but i keeping getting 12.33 when the answer is 12.59

[dc302]

Using the cosine rule:

The angle of interest is 115 degrees. (check if you have this right).

So the rule: c^2 = a^2 + b^2 - 2abcos(115)

=> c^2 = 8.2^2 + 6.7^2 - 2(8.2)(6.7)cos(115) (check your calculator is in degree mode).

Evaluate that and you should get c = 12.59.