sinA= 3/5 and C=17
Finding a and b
Their two triangles and i have to find the ratio
i just can’t seem to set up the problem right but i gave an example of one of the practice exercise that dealt with finding only (a) so i got confused with finding a and b in that question.
for example :
find a ,given sin A = 1/2, b=1
now sinA=1/2 by the Pythagoream Theorem i know that that b=sqrt3
then given that information i cross multiplied
b/a = b1/a1
sqrt3/1 = 1/a1
squr 3*a1=1
a1=1/sqrt3 then by rationlizing
i found that a1=sqrt3/3
if you know how to do these kinda of problems please help me out.
this is confusing, post the exact problem you need help with
To find the values of "a" and "b" in your given triangle, we can use the trigonometric ratio "sin A." Let's start by setting up the problem correctly.
Given that sin A = 3/5 and C = 17, we are trying to find the values of "a" and "b" in a right triangle.
From sin A = opposite/hypotenuse, we can determine that the length of the side opposite angle A is 3, and the hypotenuse is 5.
Now, let's set up the ratios to find the lengths of "a" and "b."
Using the ratio "opposite/hypotenuse" (also known as sin ratio), we have:
a/17 = 3/5 (since a is the opposite side and C is the hypotenuse)
Next, we can cross-multiply:
5a = 3 * 17 (multiplying both sides by 17 to isolate "a")
5a = 51
Now, divide both sides by 5:
a = 51/5
So the value of "a" is 10.2
To find the value of "b" in this triangle, we can use the Pythagorean theorem:
a² + b² = c²
where "c" is the hypotenuse (in this case, 17).
Substituting the values we have:
(10.2)² + b² = 17²
104.04 + b² = 289
Now, subtract 104.04 from both sides:
b² = 289 - 104.04
b² = 184.96
Finally, take the square root of both sides to find "b":
b = √184.96
b ≈ 13.59
Therefore, in the given triangle, "a" is approximately 10.2 and "b" is approximately 13.59.