Right-triangle trig
the equation for Pythagorean theorem
a² + b² = c²
what is the sine and cosine rule and area of a triangle formula?
sine rule: a/sin(A) = b/sin(B) = c/sin(C)
cosine rule: c^2 = a^2 +b^2 - 2abcosC ;
or cosC = a^2+b^2 - c^2/ 2ab
area of a triangle: A = 1/2ab sinC
A ladder leans against a wall, forming a 70° angle with the ground. What is the angle between the ladder and the wall?
20°
Name a Pythagorean triple
- 5,12,13
- 3, 4, 5
- 9, 40, 41
- 7, 24, 25
p[on a map three schools A,B and C are situated. Schools A and B are 605 meters apart. Schools B and C are 986 meters apart. Angle ABC = 108°
a. find the distance between A and C
b. find the size of angle BAC
a. AC = 1306.5
b. angle A = 45.9
A ramp makes an angle of 15° with the ground. If the ramp is 10 meters long, what is the angle between the ramp and the vertical wall?
75°
Calculate the hypotenuse of a right triangle that has a perpendicular height of 4 cm and the base equal to 3 cm.
5 cm
find the area of the non right triangle:
triangle ABC is a isosceles triangle. AB = AC = 11.8, CB = 20cm and angle ACB = 32°
a. find the area of triangle ABC
a. area = 62.5
A tree casts a shadow 20 meters long. The angle of elevation of the sun is 30°. What is the angle between the shadow and the tree?
60°
angle of elevation and depression:
Leah's mom is standing at the bottom of the slide at the playground, waiting for Leah to slide down. if the angle of elevation from the bottom of the slide is 46°, and the slide has a vertical height of 9 feet, find the length of the slide.
length of the slide = 12.5 ft
solve for all the missing lengths and angle
in triangle ABC, AC=8cm, <ACB=101° and <ABC=32
AB = 14.8
BC = 11
<BAC = 47°
A kite string is 50 meters long and makes an angle of 40° with the ground. What is the angle between the string and the vertical line from the kite to the ground?
50°
a ladder is standing on a horizontal ground and leaning against a vertical wall. The length of the ladder is 4.8 meters. the distance between the bottom of the ladder and the base of the wall is 3.2 meters.
a. using the information above, sketch a labelled diagram showing the ground, the ladder and the wall.
b. calculate the distance between the top of the ladder and the base of the wall.
c. calculate the obtuse angle made by the ladder with the ground.
b. 3.58
c. 131.8°
a. write down the length of AC
b. find the size of angle BAC
c. find the area of the flower bed
a. AC = 9m
b. <A = 38.9
c. area = 14.1
A ship is spotted at an angle of depression of 25° from the top of a lighthouse. What is the angle between the line of sight to the ship and the vertical line from the lighthouse?
65°