(a) (i) Construct a triangle $ABC$, where |AB| = 7 cm, $\angle BAC = 50^\circ$, and |AC| = 4.5 cm. (ii) Measure the length of [BC] and hence find the sum of the lengths of the sides [AC] and [BC], correct to one decimal place. |AC| = 4.5 cm |BC| = Sum = (b) State which one of the following triangles can not be constructed. Give a reason to support your answer. Triangle 1 Sides of lengths (cm) 3, 2, 9 5, 4 Triangle 2 Sides of lengths (cm) 6, 7, 15 Answer: Reason: (c) The lengths of the sides of a right-angled triangle are 5, x, and x + 1 as shown. Use the Theorem of Pythagoras to find the value of x.

Leaving Cert Mathematics Trigonometry: (a) (i) Construct a triangle $AB

(a) (i) Construct a triangle $ABC$, where |AB| = 7 cm, $\angle BAC = 50^\circ$, and |AC| = 4.5 cm - Leaving Cert Mathematics - Question 6 - 2016

Question 6

$(a)-(i)-Construct-a-triangle-$ABC$,-where-|AB|-=-7-cm,-$\angle-BAC-=-50^\circ$,-and-|AC|-=-4.5-cm-Leaving Cert Mathematics-Question 6-2016.png$

(a) (i) Construct a triangle $ABC$, where |AB| = 7 cm, $\angle BAC = 50^\circ$, and |AC| = 4.5 cm. (ii) Measure the length of [BC] and hence find the sum of the len... show full transcript

Worked Solution & Example Answer:(a) (i) Construct a triangle $ABC$, where |AB| = 7 cm, $\angle BAC = 50^\circ$, and |AC| = 4.5 cm - Leaving Cert Mathematics - Question 6 - 2016

Step 1

Construct a triangle $ABC$, where |AB| = 7 cm, $\angle BAC = 50^\circ$, and |AC| = 4.5 cm.

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Answer

To construct triangle $ABC$ , first draw line segment $AB$ measuring 7 cm. Next, using a protractor, mark angle $50^\circ$ at point $A$ . From point $A$ , draw line segment $AC$ measuring 4.5 cm to intersect the line drawn from point $A$ at point $C$ . Connect points $B$ and $C$ to complete triangle $ABC$ .

Step 2

Measure the length of [BC] and hence find the sum of the lengths of the sides [AC] and [BC], correct to one decimal place.

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Answer

After constructing triangle $ABC$ , measure the length of segment $BC$ using a ruler. Let's assume the measurement of $BC$ is found to be 5.4 cm. Therefore, the lengths of sides are:

|AC| = 4.5 cm |BC| = 5.4 cm

The sum of the lengths is:

$|AC| + |BC| = 4.5 + 5.4 = 9.9 \text{ cm}$

Step 3

State which one of the following triangles can not be constructed.

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Answer

Answer: Triangle 2

Reason: The sides 6 and 7 are not long enough to reach the side of length 15. According to the triangle inequality theorem, the sum of the lengths of any two sides must be greater than the length of the remaining side.

Step 4

Use the Theorem of Pythagoras to find the value of x.

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Answer

Using the Pythagorean theorem,

$(x + 1)^2 + x^2 = 5^2$

Expanding and simplifying:

$x^2 + 2x + 1 + x^2 = 25$ $2x^2 + 2x + 1 - 25 = 0$ $2x^2 + 2x - 24 = 0$ $x^2 + x - 12 = 0$

Factoring, we have:

$(x + 4)(x - 3) = 0$

Thus, the possible values for x are -4 and 3. Since x must be positive in the context of side lengths, we conclude that:

$x = 3$

(a) (i) Construct a triangle $ABC$, where |AB| = 7 cm, $\angle BAC = 50^\circ$, and |AC| = 4.5 cm - Leaving Cert Mathematics - Question 6 - 2016

Worked Solution & Example Answer:(a) (i) Construct a triangle $ABC$, where |AB| = 7 cm, $\angle BAC = 50^\circ$, and |AC| = 4.5 cm - Leaving Cert Mathematics - Question 6 - 2016

Construct a triangle $ABC$, where |AB| = 7 cm, $\angle BAC = 50^\circ$, and |AC| = 4.5 cm.

Measure the length of [BC] and hence find the sum of the lengths of the sides [AC] and [BC], correct to one decimal place.

State which one of the following triangles can not be constructed.

Use the Theorem of Pythagoras to find the value of x.

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