Ramsha is an architecture student in New York. She wants to measure the height of Flatiron Building using a tape measure, protractor, and laser pointer.
Heichi is painting his house. He has a feet long ladder. To reach the top of the wall, he needs to lean the ladder against the wall with a angle.
Find the distance from the bottom of the ladder to the wall.
Notice that the ladder, wall, and ground form a right triangle.
LaShay is planning to build stairs for the second floor of her house. The horizontal part of a step is called the tread. The vertical part is called the riser. The tread and riser are fixed into a stringer.
Recall that tread is the horizontal part and riser is the vertical part of a step. Therefore, tread is parallel to the ground while the riser is perpendicular.
Because the ratio of the riser to the tread is the tangent ratio can be used to write an equation for
Finally, by using the inverse of the tangent ratio, the value of can be found.
Therefore, the measure of the angle between the stairs and ground is about
Vincenzo plans to build a grain bin with a radius of feet. The slant of the roof will be He wants the roof to overhang the edge of the bin by feet.
Either the radius or the height of the cone is necessary to find the length of the slant height. By using the given information, the radius of the cone can be found immediately. Notice that the radius of the cone is the sum of the radius of the cylinder and the length of the roof overhang.
Since the radius is the adjacent side of the given angle, cosine ratio can be used to find the value of
Maya is an archaeologist working in Egypt. Recently, she discovered the ruins of a pyramid. This is kind of a big deal. Even if most of the pyramid has eroded, Maya was able to determine that the length of a side of the square base is meters.
It is known that the ancient Egyptians built only two pyramids with faces inclined at angles. Maya thinks that she has just found one of them. Using the given information, find the height of the pyramid and round the answer to the nearest meter.
Complete the ruins of the pyramid. What is the position of the height of the pyramid in relation to the given angle?
By modeling the pyramid, the given angle and its height can be shown.
Notice that the altitude and an inclined face of the pyramid form a right angle with the base of the pyramid. Because the height is opposite the given angle, either the hypotenuse or the adjacent side is needed to find the height.
Since the length of a side of the square base is known, the adjacent side can be found by dividing it by
Now that the adjacent side has been found, the tangent ratio can be used to find the opposite side's value.
Substituting the values into this ratio, the height of the pyramid can be found.
A ball bearing consists of two concentric metal circles, called bearing races, separated by metal balls. The purpose of a ball bearing is to facilitate the movement between two interacting objects within a machines such as bicycles, wheelchairs, and even household items like washing machines.
In the diagram, assume that there is no space between the metal balls. If the outer radius of the inner circle is inches, what would be the radius of a metal ball? If necessary, round the answer to one decimal place.
Assume that the radius of each metal ball is inches.
Notice that is an isosceles triangle where From here, to find the value of the measure of the vertex angle of needs to be found. Since there are metal balls, the measure of can be found by dividing by Now that the measure of the vertex angle has been found, the altitude of the base can be drawn to aid the use of trigonometric ratios. Remember, the altitude of the base of an isosceles triangle bisects the vertex angle and the base therefore can be split in half.
In this lesson, a few real-life applications of trigonometric ratios have been detailed. There are many more fields from video games to astronomy where trigonometric ratios play essential roles. Take for example, our Solar System and galaxy, astronomers use trigonometry to find the distance to stars and planets!
Astronomers measure the location of a star in the sky at one point of the year. They then measure again six months later when the Earth is on the opposite side of the Sun. In the meantime, the star moves a tiny amount compared to Earth — a phenomenon known as parallax.