In a right triangle the two acute angles add up to 90°. This means that the cosine of one angle is the sine of the other. So Y+Y+20=90, 2Y=70, Y=35°. There are other solutions but both the angles will not be acute.

Question

asked 2021-03-12

Aidan knows that the observation deck on the Vancouver Lookout is 130 m above the ground. He measures the angle between the ground and his line of sight to the observation deck as \(\displaystyle{77}^{\circ}\). How far is Aidan from the base of the Lookout to the nearest metre?

asked 2021-03-25

Find a general solution to \(\displaystyle{y}{''}+{4}{y}'+{3.75}{y}={109}{\cos{{5}}}{x}\)

To solve this, the first thing I did was find the general solutionto the homogeneous equivalent, and got

\(\displaystyle{c}_{{1}}{e}^{{-{5}\frac{{x}}{{2}}}}+{c}_{{2}}{e}^{{{3}\frac{{x}}{{2}}}}\)

Then i used the form \(\displaystyle{K}{\cos{{\left({w}{x}\right)}}}+{M}{\sin{{\left({w}{x}\right)}}}\) and got \(\displaystyle-{2.72}{\cos{{\left({5}{x}\right)}}}+{2.56}{\sin{{\left({5}{x}\right)}}}\) as a solution of the nonhomogeneous ODE

To solve this, the first thing I did was find the general solutionto the homogeneous equivalent, and got

\(\displaystyle{c}_{{1}}{e}^{{-{5}\frac{{x}}{{2}}}}+{c}_{{2}}{e}^{{{3}\frac{{x}}{{2}}}}\)

Then i used the form \(\displaystyle{K}{\cos{{\left({w}{x}\right)}}}+{M}{\sin{{\left({w}{x}\right)}}}\) and got \(\displaystyle-{2.72}{\cos{{\left({5}{x}\right)}}}+{2.56}{\sin{{\left({5}{x}\right)}}}\) as a solution of the nonhomogeneous ODE

asked 2020-12-27

Given theta is an acute angle such that sin theta = \(\displaystyle\frac{{5}}{{13}}\) find the value of tan (theta - pi\4)

asked 2020-11-26

Match each of the trigonometric expressions below with the equivalent non-trigonometric function from the following list. Enter the appropriate letter(A,B, C, D or E)in each blank

A . \(\displaystyle{\tan{{\left({\arcsin{{\left({\frac{{{x}}}{{{8}}}}\right)}}}\right)}}}\)

B . \(\displaystyle{\cos{{\left({a}{r}{\sin{{\left({\frac{{{x}}}{{{8}}}}\right)}}}\right)}}}\)

C. \(\displaystyle{\left({\frac{{{1}}}{{{2}}}}\right)}{\sin{{\left({2}{\arcsin{{\left({\frac{{{x}}}{{{8}}}}\right)}}}\right)}}}\)

D. \(\displaystyle{\sin{{\left({\arctan{{\left({\frac{{{x}}}{{{8}}}}\right)}}}\right)}}}\)

E. \(\displaystyle{\cos{{\left({\arctan{{\left({\frac{{{x}}}{{{8}}}}\right)}}}\right)}}}\)

A . \(\displaystyle{\tan{{\left({\arcsin{{\left({\frac{{{x}}}{{{8}}}}\right)}}}\right)}}}\)

B . \(\displaystyle{\cos{{\left({a}{r}{\sin{{\left({\frac{{{x}}}{{{8}}}}\right)}}}\right)}}}\)

C. \(\displaystyle{\left({\frac{{{1}}}{{{2}}}}\right)}{\sin{{\left({2}{\arcsin{{\left({\frac{{{x}}}{{{8}}}}\right)}}}\right)}}}\)

D. \(\displaystyle{\sin{{\left({\arctan{{\left({\frac{{{x}}}{{{8}}}}\right)}}}\right)}}}\)

E. \(\displaystyle{\cos{{\left({\arctan{{\left({\frac{{{x}}}{{{8}}}}\right)}}}\right)}}}\)

asked 2020-11-24

Find the exact value of y.

asked 2020-10-26

Solve the equation

\(\displaystyle{\sin{{\left({x}°-{20}°\right)}}}={\cos{{42}}}°\) for x, where 0 < x < 90

\(\displaystyle{\sin{{\left({x}°-{20}°\right)}}}={\cos{{42}}}°\) for x, where 0 < x < 90

asked 2021-01-13

The drawing shows a uniform electric field that points in the negative y direction; the magnitude of the field is 5300 N/C.Determine the electric potential difference (a) VB - VA between points A and B, (b) VC - VB between points B and C, and (c) VA - VB between points C and A.

A-C is 10.0cm, b-c is 8.0 cm, a-b is 6.0 cm. They are all in a right triangle shape. With angle b having the 90 degree angle, and electric potential is pointing down. This is problem 56 in 7th edition.

A-C is 10.0cm, b-c is 8.0 cm, a-b is 6.0 cm. They are all in a right triangle shape. With angle b having the 90 degree angle, and electric potential is pointing down. This is problem 56 in 7th edition.

asked 2020-11-16

Find the values of the variables in each right triangle.

asked 2021-02-09

Use similar triangles to find the distance across the river.

asked 2021-03-02

The lengths of the diagonals of a rectangle are represented by 8x + 3 feet and 4x + 7 feet. Find the length of each diagonal.