Find angle A in a right-angled triangle, with cos C= 4/5? (with diagram)?

[SHUTTER]

I'm really confused! I know trigonometry well enough and I know how you can use the right angle to solve the opposite sides, etc. But this easy 2 mark question is making my mind itch.

Here it is:

Ignore my working. I tried to use cosine rule, etc. too. I don't know how to find out C. By the way, the answers sheet said:

"C = 36.9, must have C stated or markedon the diagramor sinA = 54 or tanA = 34 but must haveA stated2 3 + 6 , π 2 –1 for each"

I still don't understand.

 

[ksdhart2]

Probably the easiest way to go about it is to just use the inverse trig functions. You're given that cos(C) = 4/5. So what happens if you take the inverse cosine of both sides? cos^-1(cos(C))=cos^-1(4/5). Where does that lead? Now that you know the value of two angles, use the fact that all three angles of a triangle must add up to 180 and you have the measure of angle A.

 

[Deleted member 4993]

I'm really confused! I know trigonometry well enough and I know how you can use the right angle to solve the opposite sides, etc. But this easy 2 mark question is making my mind itch.

Here it is:

Ignore my working. I tried to use cosine rule, etc. too. I don't know how to find out C. By the way, the answers sheet said:

"C = 36.9, must have C stated or marked on the diagram or sinA = 54 or tanA = 34 but must have A stated 2 3 + 6 , π 2 –1 for each"

I still don't understand.

Are you allowed to use a scientific calculator?

 

[SHUTTER]

Probably the easiest way to go about it is to just use the inverse trig functions. You're given that cos(C) = 4/5. So what happens if you take the inverse cosine of both sides? cos^-1(cos(C))=cos^-1(4/5). Where does that lead? Now that you know the value of two angles, use the fact that all three angles of a triangle must add up to 180 and you have the measure of angle A.

I know how to use inverse cosine for unknown angles but I didn't thought of this! Thank you so much! (The answer is 53.1)

(@Subhotosh Khan By the way yes I can use a scientific (?) calculator for school! )

 

[mmm4444bot]

The answer is 53.1

Good job! Now here's a tip.

When angle measurements are stated without units, it generally means radians.

We know you meant degrees, but now's a good time to get used to writing "degrees" when you report degree measurements because you're likely to be using radian measure mixed in more going forward.

The answer is 53.1 degrees (rounded) :cool: