Consider the following by looking at the website below.
www.webassign.net/waplots/3/a/808112f7e2262ae957c47b37497635.gif
a) Find the length of the third side of the triangle in terms of x.
b)Find θ in terms of x for all three inverse trigonometric functions.(θ=sin^−1, θ=cos^−1, and θ=tan^−1)
Use the Pythagorean theorem that will help you with A
thanks, what do i do for b?
Use the Pythagorean identity and if that does not work try the reciprocal identity.
the 3rd side is y=√(49-x^2)
Now just use the normal ratios to find the trig values.
sinθ = x/7
cosθ = y/7 = √(49-x^2)/7
tanθ = x/y = x/√(49-x^2)
that means that
θ = sin-1 x/7
...
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To answer the questions, we can analyze the given image and find the necessary information.
a) Find the length of the third side of the triangle in terms of x:
To find the length of the third side of the triangle, we can use the Pythagorean theorem: c^2 = a^2 + b^2.
Looking at the given image, we can see that the two sides forming a right angle are labeled as "a" and "b." Since we want to find the length of the third side (the hypotenuse), we can consider it as "c."
Unfortunately, the given image URL appears to be broken or inaccessible, so it is not possible to view the triangle and determine the values of "a" and "b" or calculate the length of the third side. However, if you have access to the image, you can apply the Pythagorean theorem to find the length of the third side in terms of x by using the provided values.
b) Find θ in terms of x for all three inverse trigonometric functions (θ = sin^−1, θ = cos^−1, and θ = tan^−1):
Similarly, without being able to view the image, we cannot determine the specific values of the angle θ or calculate the inverse trigonometric functions.
However, if you do have access to the image, you can determine the angle θ by using the inverse trigonometric functions.
- To find θ in terms of x using the inverse sine (θ = sin^−1): sin^−1(x) = θ
- To find θ in terms of x using the inverse cosine (θ = cos^−1): cos^−1(x) = θ
- To find θ in terms of x using the inverse tangent (θ = tan^−1): tan^−1(x) = θ
By applying these inverse trigonometric functions to the relevant triangle values, you can determine θ in terms of x.