5 Ways To Solving Trigonometry Problems Finding 2024

<ul> <li> Solving Trigonometry Problems Finding Ladder Length and Height Above Ground </li> </ul>

Discover a step-by-step solution to a trigonometry problem involving a ladder leaning against a wall at a 71-degree angle. Learn how to find the length of the ladder and the height above the ground using trigonometric principles.

The problem involves a ladder against a vertical wall making a 71-degree angle with the ground.
A tightrope is connected from the ladder to the ground.
We need to find the length of the ladder (AB) and the height of the ladder above point B.

In this trigonometry problem, we are tasked with determining the length of a ladder (AB) and the height of the ladder above the ground. The ladder is positioned against a vertical wall at a 71-degree angle with the ground, and it is secured by a tightrope connected from point A to the ground at point Q. We will break down the solution into steps.

Step 1 Finding Angle X We start by finding angle X, which is necessary to proceed with the calculations. Angle X can be determined by recognizing that in a right-angled triangle, the sum of its angles is equal to 180 degrees. Given that angle AQB is 90 degrees and angle AQP is 71 degrees, we can find angle X as follows

90 degrees + 71 degrees + X = 180 degrees
X = 180 degrees - 90 degrees - 71 degrees
X = 19 degrees

Step 2 Calculating Angle APQ With angle X known, we can now calculate angle APQ, which is complementary to angle AQP. The sum of complementary angles is 90 degrees, so

APQ = 90 degrees - 71 degrees
APQ = 19 degrees

Step 3 Finding Length AP (Hypotenuse) We now have a right-angled triangle with angle APQ being 19 degrees and angle PAQ being 90 degrees. To find the length of AP (the hypotenuse), we can use the trigonometric ratio of cosine

cos(19 degrees) = Adjacent / Hypotenuse
cos(19 degrees) = 1.68 meters / AP Solving for AP
AP = 1.68 meters / cos(19 degrees)
AP ≈ 1.776 meters

Step 4 Determining Length AB (Ladder) To find the length of the ladder (AB), we use the trigonometric ratio of sine in the same right-angled triangle

sin(71 degrees) = Opposite / Hypotenuse
sin(71 degrees) = AB / AP Solving for AB
AB = AP * sin(71 degrees)
AB ≈ 1.776 meters * sin(71 degrees)
AB ≈ 1.619 meters

Step 5 Conclusion The length of the ladder (AB) is approximately 1.619 meters, and the height of the ladder above the ground is approximately 1.776 meters. This solves the problem of finding the ladder's dimensions when it is leaning against a vertical wall at a 71-degree angle with the ground. Trigonometry is a valuable tool for solving such real-world scenarios. We hope this explanation has been helpful in understanding the solution to this problem. Thank you for reading, and if you found this information useful, please consider liking and subscribing for more content.

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