if tan theta =15/8 find sin theta+ cos theta
Answers
Answer:23/3cos theta
Step-by-step explanation: tan theta equals to 15 by 8 sin by cos theta equals to 15 by 8 sign equals to 15 by 8 cos theta sin theta + cos theta equals to 15 by 8 cos theta + cos theta equals to 23 by 8 cos theta
Answer:
23/17
Step-by-step explanation:
This question can be solved by considering a triangle with an angle θ made between its base and hypotenuse.
Useful and prerequisite information:
sinθ=height/hypotenuse
cosθ=base/hypotenuse
Given:
tanθ=15/8
We know that
tanθ=height/base=h/b
h/b=15/8
Therefore we can say that
h=15x
b=8x
where x is any constant
Hypotenuse of the triangle so formed would be
l=√(h²+b²)
=√((15x)²+(8x)²)
=√(225x²+64x²)
=17x
Therefore the lenght of the hypotenuse is 17x
We know that
sinθ=height/hypotenuse
=15x/17x
=15/17
and
cosθ=base/hypotenuse
=8x/17x
=8/17
Now,
cosθ+sinθ=15/17+8/17
=23/17
Hope this helps.