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7.04 Further problem solving with trigonometry

Interactive practice questions

Consider the given triangle.

A triangle with vertices labeled A, B, and C is presented. Vertex A is at the top, vertex B is on the lower left, and vertex C is on the lower right. The side opposite vertex A is labeled with the length of 18 units. The angle ABC at vertex B is labeled as 63 degrees, and the angle ACB at vertex C is labeled as 88 degrees, opposite to this angle is side AB labeled with lowercase letter '$c$c'.

a

First, find the value of $\angle BAC$BAC.

b

Find the length of $c$c.

Round your answer to two decimal places.

Easy
3min

A triangle has sides of length $13$13 cm, $15$15 cm and $5$5 cm. The largest angle has a size of $x$x$^{\circ}$. Calculate $x$x.

Round your answer to the nearest degree.

Medium
3min

Consider the following diagram:

Easy
3min

A radio signal is sent from a transmitter at tower T, via a satellite S, to a town W, as shown in the diagram. The town is $526$526 km from the transmitter tower. The signal is sent out from the transmitter tower at an angle of $18^\circ$18° , and the town receives the signal at an angle of $26^\circ$26°.

Calculate the height of the satellite above the ground.

Medium
7min
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Outcomes

4.2.1.3

establish and use the sine (ambiguous case is required) and cosine rules and the formula 𝐴rea=1/2 bc sin𝐴 for the area of a triangle

4.2.1.4

construct mathematical models using the sine and cosine rules in two- and three-dimensional contexts (including bearings in two-dimensional context) and use the model to solve problems; verify and evaluate the usefulness of the model using qualitative statements and quantitative analysis

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