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4.05 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

$\triangle ABC$ABC consists of angles $A$A, $B$B and $C$C which appear opposite sides $a$a, $b$b and $c$c respectively. Consider the case where the measures of $a$a, $c$c and $A$A are given.

Easy
1min

A parallelogram has a side of length $13$13 cm and a diagonal of length $58$58 cm. If the angle between these two is $17^\circ$17° and the length of the other side is $x$x cm, find $x$x.

Round your answer to one decimal place.

Easy
2min

Mae went for a bike ride on Sunday morning from Point A to Point B , which was $18$18 kilometers long. She then took a $126^\circ$126° turn and rode from Point B to Point C, which was $21$21 kilometers long. How far was she from her starting point?

Round your answer to two decimal places.

Easy
2min
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Outcomes

1.2.4

establish and use the sine and cosine rules, including consideration of the ambiguous case and the formula Area=1/2 bc sin⁡A for the area of a triangle

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