Die diagram hieronder toon 'n koordinate vierhoek TSQR. TS = 22 m en TR = 18 m ∠T = 67° en ∠R₁ = 42,5° Bepaal: 6.1.1 Die lengte van SR 6.1.2 Die grootte van ∠M 6.2 Beantwoord die volgende vrae met betrekking tot ΔSMR. 6.2.1 Voltooi die sinusreël: SM / sin R₁ = SR / sin M 6.2.2 Bepaal vervolgens die lengte van SM. 6.3 Die oppervlakte van ΔSMR moet bereken word. Een sak kunsmis het 15,178 vierkante meter. Bepaal die aantal sakke kunsmis wat benodig word om die oppervlakte van ΔSMR te bedek.

NSC Technical Mathematics Euclidean Geometry: Die diagram hieronder toon 'n ko

Die diagram hieronder toon 'n koordinate vierhoek TSQR - NSC Technical Mathematics - Question 6 - 2024 - Paper 2

Question 6

Die diagram hieronder toon 'n koordinate vierhoek TSQR. TS = 22 m en TR = 18 m ∠T = 67° en ∠R₁ = 42,5° Bepaal: 6.1.1 Die lengte van SR 6.1.2 Die grootte van ∠M ... show full transcript

Worked Solution & Example Answer:Die diagram hieronder toon 'n koordinate vierhoek TSQR - NSC Technical Mathematics - Question 6 - 2024 - Paper 2

Step 1

6.1.1 Die lengte van SR

96%

114 rated

Answer

To find the length of segment SR, we can use the cosine rule. The formula is given by:

$SR^2 = TS^2 + TR^2 - 2 imes TS imes TR imes ext{cos}( heta)$

Here, TS = 22 m, TR = 18 m, and $heta = 67°$ . Substituting these values:

$SR^2 = (22)^2 + (18)^2 - 2 imes (22) imes (18) imes ext{cos}(67°)$

Calculating the right-hand side yields:

$SR^2 = 484 + 324 - 2 imes 22 imes 18 imes 0.3907 ≈ 498.5409462$

Thus, taking the square root gives:

$SR ≈ 22.33 m$

Step 2

6.1.2 Die grootte van ∠M

99%

104 rated

Answer

To find the angle ∠M, we use the fact that the sum of angles in a triangle is 180°. Therefore:

$M = 180° - ∠T - ∠R₁$

Substituting the known values:

$M = 180° - 67° - 42.5° = 70.5°$

Step 3

6.2.1 Voltooi die sinusreël:

96%

101 rated

Answer

Using the sinus rule for triangle ΔSMR:

$\frac{SM}{\sin R₁} = \frac{SR}{\sin M}$

Step 4

6.2.2 Bepaal vervolgens die lengte van SM.

98%

120 rated

Answer

To find the length of SM, we can rearrange the previous equation:

$SM = \frac{SR \cdot \sin R₁}{\sin M}$

Substituting the known values:

$SM = \frac{22.33 \cdot \sin(42.5°)}{\sin(70.5°)}$

Calculating this gives:

$SM ≈ 16.39 m$

Step 5

6.3 Die oppervlakte van ΔSMR moet bereken word.

97%

117 rated

Answer

To calculate the area of triangle ΔSMR, we can use the formula:

$\text{Area} = \frac{1}{2} \cdot SR \cdot SM \cdot \sin(∠M)$

Substituting the known values:

$\text{Area} = \frac{1}{2} \cdot 22.33 \cdot 16.39 \cdot \sin(70.5°)$

Calculating this gives an approximate area, and to find the number of bags needed:

$\text{Number of bags} = \frac{\text{Area}}{15.178}$

Die diagram hieronder toon 'n koordinate vierhoek TSQR - NSC Technical Mathematics - Question 6 - 2024 - Paper 2

Worked Solution & Example Answer:Die diagram hieronder toon 'n koordinate vierhoek TSQR - NSC Technical Mathematics - Question 6 - 2024 - Paper 2

6.1.1 Die lengte van SR

6.1.2 Die grootte van ∠M

6.2.1 Voltooi die sinusreël:

6.2.2 Bepaal vervolgens die lengte van SM.

6.3 Die oppervlakte van ΔSMR moet bereken word.

Join the NSC students using SimpleStudy...