How to solve a right triangle when you know all the angles and the hypotenuse?

This is the problem. I don’t want you to solve it I just need to know how i can solve it.

Suppose you have a ladder 6.7 m long. If the ladder makes an angle of 63 degrees with the level ground when you lean it against a vertical wall, how high up the wall is the top of the ladder?

Answer #1

The trigonometric functions are are all ratios of the sides of a right triangle When you know part of the information of a triangle you can calculate the missing information by using one of the trig functions.

The mnemonic I learned in grade school to remember the ratios for sine, cosine, and tangent was “Have Oscar Heap Apples And Oranges” The ratios for sin, cos, and tan respective are H/O, H/A, A/O or hypotenuse/opposite side, hypotenuse/adjacent side, and adjacent side/opposite side.. Draw a triangle diagram of your ladder, ground, and wall. Fill in the information you know and determine what trig functions can provide the missing information. Use a calculator or trig table to get the value for the needed trig functions and do the calculations.

Answer #2

Your formula is, for the reasons specified by filletofspam:

sin(63)6.7 = X

Answer #3

Interesting! We were taught SOH CAH TOA… . Sine = Opposite ÷ Hypotenuse

Cosine = Adjacent ÷ Hypotenuse

Tangent = Opposite ÷ Adjacent

It’s weird how some things never ever leave your brain even though you use them for nothing, once you’ve completed the final exam! No wonder I can never find my car keys. My brain is full of mnemonics.

Answer #4

Your comment actually got me to look at what I wrote and I realized that I put the wrong mnemonic down. Considering that I spent a few years working on discrete cosine transforms you’d think I would get the basic functions correct!

The mnemonic for sin, cos, and tan should be “Oscar Had A Heap Of Apples”

The mnemonic I put above was for for cosecant, secant, cotangent which are 1/sin, 1/cos, 1/tan respectively. Considering that these are reciprocals of the other functions they probably do not really require a seperate mneumonic past remembering to flip the numerator and operator. I’m suffering from mnemonic overload I guess.

Sorry for any confusion; especially if it resulted in an incorrect homework answer!

Mnemonics are actually the easiest way to learn. They trick the brain into indexing the same information multiple ways for easier retrieval.

Answer #5

Oops! Its cos(63)6.7 = X

Answer #6

Because another triangle could have exactly the same angles, but its sides could all be twice as long, or 62 times as long etc.

There are an infinite number of triangles that all have the same two acute angles. They’re all similar to each other, but they’re not congruent.

http://funadvice.com/r/15dmnodmqcj

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