A. 15-foot ladder is leaning against a house so that it is 7 feet from the ground. What angle does the ladder make with the ground?
B. A plane must begin its descent when it is 80 feet above the ground and 250 feet from the airport. At what angle should his descent be if he wants to fly in a straight line from the point of descent to the ground?
A. Well, this ladder seems to have quite the angle problem. It's leaning against a house, thinking it's all cool, but little does it know that I'm about to calculate its angle. So, let's see here... The hypotenuse is the ladder, which is 15 feet long, and the opposite side is 7 feet long. To find the angle, we can use some trigonometry. The angle will be equal to the inverse tangent of the opposite side divided by the hypotenuse. So, angle = arctan(7/15). Now, I'll just pop this into my trusty calculator. *boop boop boop* Ah, there we have it! The ladder is making an angle of approximately 27.97 degrees with the ground. Hope it's not feeling too tilted about that!
B. Ah, the plane is coming in for a landing, but it wants to do it in style. It's asking about the angle it should take to fly straight from its point of descent to the ground. Well, I'm no air traffic controller, but I can surely calculate it for you. The height from the point of descent to the ground is 80 feet, and the horizontal distance from the airport is 250 feet. To find the angle, we can once again turn to trigonometry. Using the tangent function, we'll take the opposite side (height) and divide it by the adjacent side (distance). So, angle = arctan(80/250). Let's do some quick math here... *beep beep beep* Ah, the angle comes out to be approximately 17.41 degrees. So, dear plane, if you want to make a stylish descent, go for that angle and make sure to adjust your aviators too. Happy landing!
A. To find the angle that the ladder makes with the ground, we can use the trigonometric function tangent. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the ladder from the ground (7 feet) and the adjacent side is the distance of the ladder from the house (15 feet).
So, the equation becomes:
tan(angle) = opposite / adjacent
tan(angle) = 7 / 15
To find the angle, we take the inverse tangent (also known as arctan) of both sides:
angle = arctan(7 / 15)
Using a calculator, we can find that the angle is approximately 26.57 degrees.
Therefore, the angle that the ladder makes with the ground is approximately 26.57 degrees.
B. To find the angle at which the plane should descend, we can use the trigonometric function tangent. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the altitude at which the plane begins its descent (80 feet) and the adjacent side is the horizontal distance from the point of descent to the airport (250 feet).
So, the equation becomes:
tan(angle) = opposite / adjacent
tan(angle) = 80 / 250
To find the angle, we take the inverse tangent (also known as arctan) of both sides:
angle = arctan(80 / 250)
Using a calculator, we can find that the angle is approximately 17.18 degrees.
Therefore, the angle at which the plane should descend is approximately 17.18 degrees.
To solve these problems, we can use basic trigonometric functions such as sine, cosine, and tangent.
A. To find the angle that the ladder makes with the ground, we can use the inverse tangent function (also known as arctan or atan). The inverse tangent function allows us to find the angle when given the opposite and adjacent sides of a right triangle. In this case, the ladder forms the hypotenuse, and we know that the ladder is 15 feet long and leaning against the house 7 feet above the ground.
By setting up the equation: tan(angle) = opposite / adjacent,
we can plug in the given values: tan(angle) = 7 / 15.
To find the angle, we can use the inverse tangent function to solve for angle:
angle = arctan(7/15).
Using a scientific calculator or an online calculator with inverse trigonometric functions, we can find the angle to be approximately 26.57 degrees.
B. To find the angle of descent, we can use the same trigonometric concept. The plane wants to fly in a straight line from the point of descent to the ground. The distance between the point of descent and the airport is 250 feet, and the plane starts its descent when it is 80 feet above the ground.
We can set up a right triangle, with the angle of descent being the angle we want to find. The opposite side is the height (80 feet), and the adjacent side is the distance to the airport (250 feet).
By setting up the equation: tan(angle) = opposite / adjacent,
we can plug in the given values: tan(angle) = 80 / 250.
To find the angle, we can use the inverse tangent function to solve for the angle:
angle = arctan(80/250).
Using a scientific calculator or an online calculator with inverse trigonometric functions, we can find the angle to be approximately 18.29 degrees.
Looks like you need to review your basic trig functions.
As always , draw a diagram!
A. sinθ = 7/15
B. tanθ = 80/250