Solving Multl-Step Equations (continued)

Veronica made a triangle by taking an 8 \(1/2 \times; 11\) sheet of paper and putting a dot at the top. She then drew lines from the bottom corners to the dot and cut along the lines (see diagram). [Triangles] What is the area of the triangle that Veronica cut out?

If the hypotenuse of a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle has a length of \(\displaystyle\sqrt{2}\), how long are the legs?

In triangle ABC, \(a=15\), \(b=14\), \(c=10\). Find \(\displaystyle{m}{<}{B}\)

Suppose that you are headed toward a plateau 50 meters high. If the angle of elevation to the top of the plateau is \(60^{\circ}\), how far are you from the base of the plateau?

In general, \(\tan(\alpha+\beta)\) is not equal to \(\tan\alpha+\tan\beta\). However, there are some values of \(\alpha\) and \(\beta\) for which they are equal. Find such \(\alpha\) and \(\beta\) and do the same for \(\tan(\alpha-\beta)\)

Find the point on the line \(y=5x+3\) that is closet to the origin.

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 \(77^{\circ}\). How far is Aidan from the base of the Lookout to the nearest metre?

The leg of a right triangle that lies on one ray of angle \(\theta\) is called the ? leg, and the leg that lies across triangle from \(\theta\) is called the ? leg.