Question Type 4: Using cosine rule to find the 3rd side Exercises

In triangle BCD, $BC = 8$, $CD = 6$, and $\angle BCD = 65^\circ$. Compute $BD$ to one decimal place.

In triangle XYZ, $XY = 6$, $XZ = 8$, and angle $YXZ = 65^\circ$. Calculate the length of $YZ$ to one decimal place.

Triangle CAT has $CA = 6$, $CT = 8$, and $\angle ACT = 65^\circ$. Find $AT$ to the nearest tenth.

In triangle ABC, $AB = 6$, $AC = 8$, and $\angle BAC = 65^\circ$. Calculate the length of $BC$ to one decimal place.

In triangle RSP, $RS = 6$, $RP = 8$, and $\angle SRP = 65^\circ$. Determine $SP$ to one decimal place.

In triangle DEF, $DE = 6$, $DF = 8$, and $\angle EDF = 65^\circ$. Determine $EF$ correct to two decimal places.

In triangle UVW, $UV = 8$, $VW = 6$, and $\angle UVW = 65^\circ$. Calculate $UW$ to two decimal places.

In triangle PQR, $PQ = 8$, $PR = 6$, and angle $QPR = 65^\circ$. Find the length of $QR$ to two decimal places.

Triangle EFG has $EF = 6\,\mathrm{m}$, $EG = 8\,\mathrm{m}$, and $\angle FEG = 65^\circ$. Find $FG$ to two decimal places.

In triangle JKL, $JK = 8$, $JL = 6$, and $\angle KJL = 65^\circ$. Calculate $KL$ to two decimal places.

Triangle QRS has $QR = 6\,\mathrm{cm}$, $RS = 8\,\mathrm{cm}$, and $\angle QRS = 65^\circ$. Determine $QS$ correct to three significant figures.

Triangle MNO has $MN = 8$, $MO = 6$, and $\angle NMO = 65^\circ$. Find $NO$ to three significant figures.