Finding Missing Lengths - Grade 12 Geometry

A Grade 12 math worksheet on finding missing lengths using advanced geometric principles, including trigonometry, similar triangles, and the Pythagorean theorem.

Grade 12 Math GeometryFinding Missing Lengths

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Includes

2 Short AnswerFill in the BlanksMultiple Choice

Standards

CCSS.MATH.CONTENT.HSG.SRT.C.8CCSS.MATH.CONTENT.HSG.SRT.B.5CCSS.MATH.CONTENT.HSG.SRT.D.11

Topics

GeometryMissing LengthsTrigonometrySimilar TrianglesPythagorean TheoremGrade 12

6 sections · Free to use · Printable

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Finding Missing Lengths - Grade 12 Geometry

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Read each question carefully and solve for the missing lengths. Show all your work and round answers to two decimal places where necessary.

1. A ladder 15 meters long leans against a wall. The base of the ladder is 5 meters from the wall. How high up the wall does the ladder reach?

2. From the top of a 100-foot lighthouse, the angle of depression to a boat out at sea is 25 degrees. How far is the boat from the base of the lighthouse?

3. Two triangles are similar if their corresponding angles are and their corresponding sides are .

4. If triangle ABC is similar to triangle DEF, and AB = 6 cm, BC = 8 cm, and DE = 9 cm, then EF = cm.

5. A right triangle has legs of length 7 cm and 24 cm. What is the length of the hypotenuse?

25 cm

31 cm

17 cm

576 cm

6. A rectangular field is 80 meters long and 60 meters wide. What is the length of the diagonal across the field?

7. An equilateral triangle has a perimeter of 36 cm. What is the length of its altitude?