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Right triangles and trigonometry

### Solving Multl-Step Equations (continued)

Right triangles and trigonometry

### Tell whether two angles can be as described. Justify your answers. a. vertical and complementary b. vertical and supplementary c. complementary and supplementary

Right triangles and trigonometry

### Draw a triangle that satisfies the set of conditions. Then classify the triangle. a triangle with three acute angles and three congruent sides.

Right triangles and trigonometry

### Veronica made a triangle by taking an 8 $$\frac{1}{2} \times 11$$ 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). What is the area of the triangle that Veronica cut out?

Right triangles and trigonometry

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

Right triangles and trigonometry

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

Right triangles and trigonometry

### 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?

Right triangles and trigonometry

### Two college friends are taking a weekend road trip. Friday they leave home and drive 87 miles north for a night of dinner and dancing in the city. The next morning they drive 116 miles east to spend a day at the beach. If they drive straight home from the beach the next day, how far do they have to travel on Sunday?

Right triangles and trigonometry

### [Triangle] Find the value of x and y.

Right triangles and trigonometry

### Find, correct to the nearest degree, the three angles of the triangle with the given vertices. A(1,0,-1), B(5,-3,0), C(1,5,2) Find $$\angle CAB,\angle ABC, \angle BCA$$

Right triangles and trigonometry

### 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 $$\tan(\alpha-\beta)$$

Right triangles and trigonometry

### A classmate drew an acute triangle with sides 9 in. and 12 in. What is the greatest possible whole number that can be the length of the longest side of the triangle in inches? Provide evidence.

Right triangles and trigonometry

### Find an equation of the plane. The plane through the points (2, 1, 2), (3, −8, 6), and (−2, −3, 1)

Right triangles and trigonometry

### At what point do the curves $$r_1(t)=t,4-t,35+t^2$$ and $$r_2(s)=7-s,s-3,s^2$$ intersect? (x,y,z)= Find angle of intersection, $$\theta$$, correct to the nearest degree.

Right triangles and trigonometry

### Find the point on the line $$y=5x+3$$ that is closet to the origin.

Right triangles and trigonometry

### In triangle DEF, side E is 4 cm long and side F is 7 cm long. If the angle between sides E and F is 50 degrees, how long is side D?

Right triangles and trigonometry

### 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?

Right triangles and trigonometry

### 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.

Right triangles and trigonometry