Solving Triangles with Given Information

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Solving Triangles with Given Information — Free MYP4 Mathematics (Extended) Practice Questions

1QuestionWorking with Two Sides and Included Angle SASConcept Practice

2 marks~3 minCriterion A

A surveyor measures two boundary lines from a fixed point

A

: line

AB = 5 \text{ cm}

and line

AC = 7 \text{ cm}

, with

\angle BAC = 40°

.

Calculate the length of

BC

, giving your answer correct to 3 significant figures. [2]

Solutions

2QuestionMultiple Solutions in Ambiguous SSA CasesAssessment Practice

2 marks~3 minCriterion C

A surveyor models a triangular plot of land

ABC

, where

AB = 8\ \text{cm}

AC = 6\ \text{cm}

, and

\angle ABC = 30°

Calculate the perpendicular height

h

from vertex

B

to side

AC

. [1]

The surveyor claims only one triangular plot is possible. Justify whether this claim is correct, referring to the relationship between

h

AC

, and

AB

. [1]

Solutions

3QuestionWorking with Two Sides and Included Angle SASAssessment Practice

4 marks~6 minCriterion B

A landscape architect designs triangular garden plots, each with two sides of lengths

a

and

b

and a fixed included angle of

35°

. The table shows how the area changes as the product of the side lengths increases.

$ab$ (cm²)	20	40	60	80	100	120
Area (cm²)	5.7	11.5	17.2	23.0	28.7	34.5

State the formula for the area of a triangle given two sides and their included angle. Hence calculate the constant of proportionality

k

when the included angle is

35°

. [1]

Analyse the data to show that area is directly proportional to

ab

, and determine the constant of proportionality from the data. [2]

The architect needs a plot with an area of at least 40 cm². Justify whether a plot with side lengths

a = 12

cm and

b = 11

cm is sufficient to meet this requirement. [1]

Solutions

4QuestionSolving ASA and AAS Triangle SituationsAssessment Practice

4 marks~6 minCriterion D

A surveyor needs to find the width of a river. She stands at point

A

on one bank and sights a tree

T

on the opposite bank, where the angle between the riverbank and

AT

90°

. She walks

50

m along the bank to point

B

and measures the angle

ABT = 38°

. The riverbanks are straight and parallel.

Calculate the width of the river

AT

. Show all working. [2]

Each angle measurement has a possible error of

\pm 0.5°

. Calculate the range of possible widths of the river. [1]

The surveyor's manager requires a measurement accurate to within

\pm 1

m. Evaluate whether the surveyor should submit this result or take additional measurements, justifying your answer with reference to the angular error and at least one real-world limitation of the model. [1]

Solutions

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