Trigonometry

Slides by Engr. Gerard Vincent P. Batusin

Problem 1: Heron's Formula

Two sides of a triangle measure 8cm and 12cm. Find its area if its perimeter is 26cm.

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Problem 2: Worded Problem (Unknown Altitudes)

Two triangles have equal bases. The altitude of one triangle is 3 units more than its base and the altitude of the other is 3 units less than its base. Find the altitudes, if the areas of the triangle differ by 21 square units.

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Problem 3: (Bisected Longest Line - Area of Adjacent Side)

A triangular piece of wood having a dimension 130 cm, 180 cm, and 190 cm is to be divided by a line bisecting the longest side drawn from its opposite vertex. The area of the part adjacent to the 180 cm side is:

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Problem 4: Area of Larger Segment of a Circle

A circle whose area is 452 cm square is cut into two segment by a chord whose distance from the center of the circle is 6 cm. Find the area of the larger segment in cm square.

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Problem 5: Height of the Tower (Right Triangles)

A man finds the angle of elevation of the top of a tower to be 30 degrees. He walks 65m nearer the tower and finds it angle of elevation to be 60 degrees. What is the height of the tower and its distance from the first position of the man?

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Problem 6: Tilted Piece of Wood

A rectangular piece of wood 4 cm x 12 cm tall is tilted at an angle of 45°. Find the vertical distance between the lower corner and the upper corner.

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Problem 7: Height of Tower (Right and Oblique Triangles)

Towers 𝐴 and 𝐵 stands on a horizontal plane, tower B being 150 m high. The angle of elevation of the top of tower 𝐴 as seen a point 𝐶 in the plane (in the same vertical plane with 𝐴 and 𝐵) is 50°. The angle of depression of 𝐶 viewed from the top of tower 𝐵 is 27.5°. The angle subtended at the top of tower 𝐵 by the top of tower 𝐴 and 𝐶 is 50°. Find the height of tower 𝐴.

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Problem 8: Elevation of Mountain Peak B

A mountain peak A is 1,040 m above sea level. From mountain peak A, the angle of elevation of mountain peak B was 10 degrees. The pilot of Air Asia upon flying directly over peak A, took the angle of depression of peak B equal to 46°12’ and read his altimeter to be 2,820 m above the sea level. Determine the elevation of mountain peak B.

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Problem 9: Two Ships Leaving the Port at the Same Time

Two ships leave port at the same time, one ship sailing in the direction N 23º E at a speed of 11 miles per hour, and the second ship sailing in the direction of S 67º E at 15 mph. Find the bearing from the second ship to the first ship after one hour of travel.

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Problem 10: Distance Between the Ship Wreck and Tower (Bearings)

From a boat sailing due north at 16.5 kph a wrecked ship K and an observation tower T are observed in a line due east. One hour later the wrecked ship and the tower have bearings S 34°40’ E and S 65°10’ E. Find the distance between the wrecked ship and the tower.

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Problem 11: Intersecting Tangents Theorem

Refer to the image:

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Problem 12: Intersecting Tangent and Secant

A road is tangent to a circular lake. Along the road and 15 kilometers from the point of tangency, another road opens towards the lake. From the intersection of the two roads to the periphery of the lake, the length of the new road is 11.5 kilometers. If the new road will be prolonged across the lake, find the length of the bridge to be constructed.

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Problem 13: Intersecting Secants

PQ and RS are secants of a circle which when extended beyond "Q" and "S" intersect at a point "T" outside the circle. Given that arc PR = 105° and arc QS = 67°, find angle "QTS".

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