# How To Solve Trigonometric Problems

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In fact, it forms the side of two right angle triangles – since two different angles were measured.

Unlike the previous example, we don’t know the length of the other side, but we do know the length of the measuring stick – it is 2 m.

The tree and its shadow form another right angle triangle.

The rays of the sun (which are invisible) form the hypotenuse of these right angle triangles.

We know the angle the sun makes with the ground, so we know one of the angles of the triangle (actually, we know two of them – the other is 90° – so, if we need to, we can find the third angle because all angles in a triangle must sum up to 180°).

All right angle triangles with the same angles are similar triangles – it doesn’t matter if we don’t know the lengths of the sides because we know the ratios those sides will have.As before, we know that: A surveyor measuring the height of the cliff, determines that the angle to the top of the cliff is 60° – this angle was measured at a height of 1.7 m (i.e. We’re not finished with the height of the cliff lighthouse, the angle to the top of the cliff lighthouse was measured from a height of 1.7 m, this means we need to add 1.7 m to the height of the cliff lighthouse: In this example, it was not necessary to correct the height of the cliff and cliff lighthouse by adding 1.7 m to each because each was offset (measured) from the same point – but it is still good practice to find the true heights (dimensions) even if only the relative ones are good enough. One surveyor stands at one end of the field with the measuring equipment, the other surveyor stands at the other end of the field with a measuring stick 2 m high. The measuring stick (or part of it) forms another side.the surveying equipment is on a tripod and stands 1.7 m above the ground). The surveyor measures an angle of 2° to the base of the measuring stick. Finally, the line of sight to the base of the measuring stick forms the remaining side (which is also the hypotenuse): We know the height where the straight line of sight intersects the measuring stick must be 1.7 m.In these lessons, examples, and solutions we will learn the trigonometric functions (sine, cosine, tangent) and how to solve word problems using trigonometry. Step 5: Consider whether you need to create right triangles by drawing extra lines.Related Topics: More Lessons on Trigonometry Trigonometry Games The following diagram shows how SOHCAHTOA can help you remember how to use sine, cosine, or tangent to find missing angles or missing sides in a trigonometry problem. For example, divide an isosceles triangle into two congruent right triangles.We now know the length of one of the sides of the Simplifying everything we get: height = 146.7 m To calculate the elevation of the sun, we know the ratio of height to length.In trigonometric terms, this is the definition of tangent. Looking up (or using the inverse key on the calculator) we see that for tanα to equal 1.111…, α must be 48°. On July 1st, 2012, at noon, the sun’s angle of elevation was 67.6°. We know the height of the tower and we know the angle of the sun (relative to the ground).Using his 2 m measuring stick he notices that it casts a shadow of 1.8 m. We know the length of the shadow to the base of the pyramid, but we need to know the length of the shadow to the center of the pyramid (from which the height is measured).If the great pyramid measures 230 m on a side, how high is the great pyramid? We know the length of a side of the pyramid (this 230 m), we can use this to determine what the length of the shadow to the center of the pyramid should be.We know that the following must be true: This is similar to calculating the length of the shadow from two examples earlier.The distance from the cliff, with the height of the cliff and the straight line to the top of the cliff form a right angle triangle. We also know that all right angle triangles with the same angle are similar triangles – this means we also know the ratios the various sides of the triangles have. The straight line (of sight) to the measuring stick is perpendicular to the measuring stick, therefore, it forms one side of a right angle triangle.