Topics
Trigonometry
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New Zealand
Level 6 - NCEA Level 1

Applications to Geometry

Lesson
Practice

Interactive practice questions

Consider the following figure.

A scalene triangle is divided into two by an internal segment represented by a dashed line which measures 5 and is perpendicular to the base of the triangle. A right triangle is formed on the right hand side which has a hypotenuse of 10 and its base is labeled as y. Another right triangle is formed on the left hand side which has a hypotenuse of 7 and its base is labeled as x.

a

Find the value of $x$x.

Round your answer to two decimal places.

b

Next, find the value of $y$y.

Round your answer to two decimal places.

c

Hence or otherwise, find the length of the base of the triangle.

Round your answer to two decimal places.

Easy
3min

Consider the following diagram.

Easy
3min

Consider the following trapezium.

Easy
3min

Consider a cone with slant height $13$13m and perpendicular height $12$12m.

Easy
1min
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Outcomes

GM6-6

Use trigonometric ratios and Pythagoras’ theorem in two and three dimensions

GM6-7

Use a co-ordinate plane or map to show points in common and areas contained by two or more loci

91031

Apply geometric reasoning in solving problems

91032

Apply right-angled triangles in solving measurement problems

91033

Apply knowledge of geometric representations in solving problems

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