Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**Hrslvr1612****Member**- Registered: 2005-12-12
- Posts: 13

10) In ΔRST, the measure of angle S is 142°. the length of line RS is 10. Find the length of the altitude from vertex R.

please help

greatly appreciated!!!

Offline

**liuv****Member**- Registered: 2006-05-14
- Posts: 29

ΔRST is not one an only:(

I'm from Beijing China.

Offline

**Sammmm****Guest**

This is a complex problem - one which scientists have pondered over for years. I have recently discovered the truth, the solution to the problem.

As I was playing football with acquantinces, I realized that the ball I was playing with, was in fact a spherical shape. I delved further into this discovery and realized that it was a 360 degree shape. I took this one step furhter and realized that the same concept applied to all shapes and that the sum of all angles in a triangle is 180 degrees. So back to your problem:

180/3 and R is 142 that means that the sum of ST is 180-142.

So S is the square root of the altitude of the vertex of the squared root of the sum.

Evident as it now may be, I will spell it out to you. The answer is 16.

Yours sincerely,

Professor Adam Eugene Cornvy III. At the University of Oxbridge.

**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 24,038

I tried to make a diagram of the triangle in the problem. The altitude from vertex R lies outside the triangle!

Let the altitude from vertext R meet ST at point P.

Angle RSP 180 - Angle RST = 180 - 142= 38 degrees

Sin (Angle RSP) = PR/RS

Sin 38 = PR/RS,

we know RS = 10

Therefore, PR = 10 sin 38 = 10(0.61566)=6.1566

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline