Solving For Right Triangles With A Twist

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• tomtomtom1
In summary, the person is seeking help to determine the clearance between a point on the ground and a wall. They have two points, A and B, with A being 30mm higher than B. They have also measured the horizontal and vertical distances from these points to the nearest point on the wall. They are now looking for the new horizontal and vertical distances after rotating point A 90mm higher than point B. They have been working on the problem for a few days and have provided a picture for reference. They are seeking advice and clarification on the wall's angle and the horizontal distance from point B to the wall. The person also mentions using a CAD or geometric tool to help solve the problem.
tomtomtom1
Hello Community

Firstly this is not a homework question despite the problem appearing to be very homework like.

I work in engineering. I am trying to determine the amount of clearance I have from a point on the ground to a wall.

I have two points, Point A and Point B.
Point A is 30mm Higher than Point B.
If I measure horizontally in the plane of points A and B to the nearest point on the wall I get 650 and vertically I get 800.
If I was to rotate point A about Point B such that Point A is now 90mm higher then Point B what would my new horizontally and vertical distance to the wall be?

After a few days working on this problem I cannot seem to make any progress.

Attached is a picture of the problem.

Can someone shed any light?

Thank You.

Attachments

• Problem.png
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Is the wall at an angle? I guess you've never done any geometry?

tomtomtom1 said:
Hello Community

Firstly this is not a homework question despite the problem appearing to be very homework like.

I work in engineering. I am trying to determine the amount of clearance I have from a point on the ground to a wall.

I have two points, Point A and Point B.
Point A is 30mm Higher than Point B.
If I measure horizontally in the plane of points A and B to the nearest point on the wall I get 650 and vertically I get 800.
If I was to rotate point A about Point B such that Point A is now 90mm higher then Point B what would my new horizontally and vertical distance to the wall be?

After a few days working on this problem I cannot seem to make any progress.

Attached is a picture of the problem.

Can someone shed any light?

Thank You.
PeroK said:
Is the wall at an angle?
Yeah, and what angle is the wall tilted forward with? And can you label the horizontal distance from the right-most point "B" to the wall?

The Blue and Red arrows are pointed to a single point on the wall.

The sloped line on the wall has no importance as each wall varies in shape, so you can imagine the sloped line of the wall not really there.

Regarding comment "And can you label the horizontal distance from the right-most point "B" to the wall?" no other information is available other then what is shown on the picture.

From the information I can derive:-
the angle at point B of the blue and red lines
The adjacent sides of the red and blue triangles.

Which sloped line do you mean?

The given measurements are sufficient to find A and B. If in doubt, introduce a coordinate system and find the coordinates of every point, and angles if relevant.

Do you have CAD available ? If you do then this problem can easily be solved graphically .

1. How do you solve for right triangles with a twist?

To solve for right triangles with a twist, you will need to use the Pythagorean theorem, trigonometric functions, and possibly the laws of sine and cosine. It is important to also identify the known and unknown sides and angles of the triangle before beginning the problem.

2. What is the Pythagorean theorem and how is it used in solving for right triangles with a twist?

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This theorem is used in solving for right triangles with a twist by providing a relationship between the sides of a right triangle and allowing us to find missing lengths or angles.

3. How do you use trigonometric functions to solve for right triangles with a twist?

Trigonometric functions such as sine, cosine, and tangent can be used to solve for missing sides and angles in right triangles. By knowing the ratio of the sides of a right triangle, we can use inverse trigonometric functions to find the missing angle or side length.

4. When do you use the law of sine and cosine in solving for right triangles with a twist?

The laws of sine and cosine are used when we are given three sides or angles of a triangle and need to find the remaining unknowns. These laws involve using trigonometric ratios and proportions to solve for the missing sides and angles.

5. Can you provide an example of solving for right triangles with a twist?

Sure! Let's say we are given a right triangle with a hypotenuse of length 10 and one angle measuring 30 degrees. We can use the Pythagorean theorem to find the length of the other leg: 10^2 = (x)^2 + (x*sin(30))^2. Solving for x, we get x = 5*sqrt(3). Then, we can use trigonometric functions to find the remaining angles and sides.

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